Mental Stress Management Using fNIRS Directed Connectivity and Audio Stimulation

In this study, we propose a method to enhance cognitive vigilance and mitigate mental stress in the workplace. We designed an experiment to induce stress by putting participants through Stroop Color-Word Task (SCWT) under time constraint and negative feedback. Then, we used 16 Hz binaural beats auditory stimulation (BBs) for 10 minutes to enhance cognitive vigilance and mitigate stress. Functional Near-Infrared Spectroscopy (fNIRS), salivary alpha-amylase, and behavioral reactions were used to determine the stress level. The level of stress was assessed using reaction time to stimuli (RT), accuracy of target detection, directed functional connectivity based on partial directed coherence, graph theory measures, and the laterality index (LI). We discovered that 16 Hz BBs mitigated mental stress by substantially increasing the target detection accuracy by 21.83% ( ${p} < 0.001$ ) and decreasing salivary alpha amylase levels by 30.28% ( ${p} < 0.01$ ). The partial directed coherence, graph theory analysis measures, and LI results indicated that mental stress decreased information flow from the left to the right prefrontal cortex under stress, whereas the 16 Hz BBs had a major impact on enhancing vigilance and mitigating mental stress via boosting connectivity network on the dorsolateral and left ventrolateral prefrontal cortex.

body's response to mental, physical, and emotional stimuli [1]. According to the Global Organization for Stress, 80% of people are experiencing stress at their workplace. Thus, stress contribute to a variety of illnesses such as cognitive difficulties, stroke, cardiovascular disease, speech abnormalities, and depression [2]. Acute stress, episodic stress, and chronic stress are the most common types of stress in the workplace.
Developing a technique for early detection of mental stress is an important component in the therapeutic intervention to prevent numerous health issues. Examining the reflection of different stressors on brain activity is one of the most innovative techniques to detect stress in its early stage. The term brain activity refers to the activity of neurons in a confined location as a consequence of a certain cognitive function. Hence, many neuroimaging techniques, such as Electroencephalography (EEG), Positron Emission Tomography (PET), and functional Magnetic Resonance Imaging (fMRI) were used to monitor the brain activity and assess the level of stress. However, fMRI and PET techniques had implementation difficulties in order to obtain accurate results, particularly when dealing with real-life stress monitoring [3], [4], [5]. Methods such as EEG, which depends on the electrical field generated by neurons in the brain, has a high temporal resolution, but its limited spatial resolution makes determining the source of activation and the associated activity pathway problematic [6]. In comparison, fNIRS promises an alternate method for detecting mental stress because it has better spatial resolution than EEG and better temporal resolution than fMRI [7]. Conversely, only few researches have used this technique individually [8], while the majority have combined it with EEG and Electrocardiogram (ECG) [9], [10].
There have been numerous studies that used fNIRS as a principal method for identifying cortical activity utilizing a variety of characteristics, stressors, and brain areas. Shi et al. [8] used several virtual training scenarios to the impact of mental stress on workers and found a large activation in the prefrontal cortex (PFC), which was then used to detect stress at a rate of 80% accuracy. Meanwhile, Mücke et al. [11] used Trier Social Stress Test (TSST) to examine the impact of psychosocial stress on cognition. The study found that maintaining a high level of physical activity did not guarantee greater inhibitory control in male teenagers exposed to psychosocial stress. Furthermore, studies in [12], [13], and [14] utilized mental arithmetic tasks as a stressor and proved the fNIRS's capability as a tool for early diagnosis and quantification of mental stress. In addition, the studies found that fNIRS could detect stress levels at accuracy within the range of 85.00% to 96.00% [12], [13], [14]. Recently, brain connectivity analysis had raised interest in dealing with fNIRS signals. In this regard, researchers often used the bivariate Pearson's correlation analysis in the time domain or its frequency domain equivalent, coherence [8], [15], [16]. While these studies have shown their capacity to discriminate between healthy and diseased populations, they have two significant limitations: first, they ignore the directionality of the relationship between brain areas of interest. Identifying the direction of information flow would help in placing the neurostimulation on the head of people having mental disorders and learning difficulties. Second, previous fNIRS time series analysis of brain activity is often confined to two signals (bivariate analysis) [8], [15], [16]. The bivariate analysis looks at two paired data sets and studies whether a relationship exists between them. Using multivariate analysis allow the use of two or more variables and analyzed which, if any, are correlated with a specific outcome. The goal in the latter case is to determine which variables influence or cause the outcome.
Moreover, several studies have used graph theory analysis (GTA) to evaluate the connectivity network between all brain areas separately. For the time being, most research is descriptive in nature, focusing only on pairwise interactions that result in graphs with dyadic linkages. However, graph theory's power, as applied to brain networks, is substantially more than what is currently being used. Nevertheless, fNIRS was recently coupled with GTA to effectively disclose the topographical structure of functional connectivity in the human brain during resting state [17], [18]. Zhang et al. [19] revealed different small-world characteristics in the frontal cortical regions when subjects engaged in deceptive behavior relative to their awake rest. Meanwhile, Li et al. [20] used GTA and demonstrated alterations in the anterior cortical areas associated with aging. This study proposes a novel technique to quantify four cognitive states using fNIRS directed connectivity, estimated by partial directed coherence (PDC), in conjunction with their respective GTA measurements based on node degree, clustering coefficient, modularity and efficiency. By doing so, we can accurately quantify the strength of the connectivity network, measure the degree to which nodes in the graph tend to cluster together, and measure the strength of division of a network into modules under four different mental states.
The neuroimaging investigations have shown evidence of cognitive disruption caused by stress, resulting in the deterioration of physical and mental health. However, stress treatment has remained marginal in medical practice due to a lack of recognized strategies for stress reduction. Therefore, the purposeful use of medicinal, therapeutic, or technological interventions to improve behavioral performance and cognitive processing is referred to as stress mitigation [21]. Several studies in the literature have explored numerous cognitive enhancers to reduce stress levels. Some of these stress-reduction techniques are commonplace and are frequently incorporated into everyday living routines such as sports, diet, meditation, odor exposure, and chewing gum [22]. On the other hand, bio-feedback method allows us to control physiological changes and visualize the results of stress mitigation in the real-time. Likewise, neurofeedback (NFB) method employs real-time recordings of brain activity to improve selfregulation of certain brain processes associated with behavior [23], [24]. EEG, fMRI, and fNIRS are the most widely utilized NFB methods [22]. The basic idea is that by training the brain with such feedback, one may entrain, alter, and regulate neural activity. While these types of stress mitigation approaches provide real-time input, they are not appropriate for use in the workplace.
Therefore, recent studies have focused on utilizing auditory stimulation such as pure tone [25] and binaural beats to enhance behavioural performance. Auditory stimulation is a kind of stimulation that can enrich the environment to improve arousal and awareness state of people. Likewise, binaural beats therapy is an emerging form of sound wave therapy. It makes use of the fact that the right and left ear each receives a slightly different frequency tone, yet the brain perceives these as a single tone. The BBs has been recently used to improve vigilance and alleviate stress at the workplace [26], [27]. Studies in [28], and [29] have shown that synchronization of brain signals and BBs caused particular changes in the mental and cognitive state. Similarly, Reedijk et al. [26] showed that BBs had a substantial influence on subject control and visual attention, whereas Lorenza et al. [30] found that BBs with a high frequency (40 Hz) tend to diminish participants' attentional processing. Interestingly, it has been demonstrated that high-frequency BBs are associated with alertness, while lowfrequency beats are associated with mental relaxation [31]. Alternatively, Goodin et al. [32] found no improvement in the mental state or performance after using BBs for times shorter than 2 minutes.
There are some promising discoveries in the literature about BBs's capacity to improve general cognitive performance and increase pain thresholds. Previous magnetoencephalography (MEG) study showed that listening to 16 Hz for 15 minutes had significantly enhanced training outcome and mitigated attentional blink, a phenomenon that reflects temporal limitations in the ability to deploy visual attention [33]. Accordingly, Robison et al. [34] reported that 16-Hz BBs had a positive effect on performance in the psychomotor vigilance task and demonstrated faster response time to stimuli. These studies inspired us to employ 16 Hz to entrain numerous mental states, including heightened alertness and reduced mental stress. Hence, the purpose of this study is to analyze and localize the changes in cerebral connectivity between different brain regions using the PDC, GTA and the LI while listening to 16 Hz BBs for 10 minutes. Likewise, a datadriven thresholding approach that is based on maximizing the Global Cost Efficiency (GCE) was used in order to filter the connectivity networks. Hence, the directionality of information flow between the two hemispheres under different mental states would be reflected by analyzing the PDCs. A computerized version of SCWT was employed to induce stress on participants and 16 Hz BBs is proposed as a stress mitigation method. Based on the above, the main contributions of this study are listed below: 1. assess mental stress levels based on graph theory analysis of fNIRS-directed connectivity network.
2. investigate the effectiveness of using binaural beats stimulation in improving cognitive vigilance and reducing mental stress. The structure of this paper is as follows. Section II describes the participation criteria, mental stress task, experimental paradigm, fNIRS recording system, data acquisition, fNIRS pre-processing, functional connectivity, graph theory analysis and statistical analysis. Section III provides a thorough analysis of the data linked to alpha amylase levels, behavioral data, subjective data, connectivity strength, directionality of information flow, graph theory analysis measures, and laterality index. This study is discussed and concluded in sections IV and V with a review of significant research findings and recommendations for future study areas.

A. Subjects
Thirty healthy volunteers from the American University of Sharjah were recruited for the study (5 females and 25 males). Eligible participants were healthy right-handed people with normal vision, hearing and color perception who have not used any long-term medicine, had any evidence of drug addiction, and who have not had any coffee, energy drinks or alcohol for at least 12 hours before the experiment. Everyone was seated in a plush chair in a cool area with plenty of ventilation.
In addition to the detailed information on the task's purpose, each participant also saw a presentation with a brief summary of the experiment's process, as well as a statement stating that they had the right to quit the session at any time. Prior to the test, the participants signed a typed consent form with their name as a signature. To avoid the effects of circadian rhythm on cognitive function, the experiment was only conducted between 1 and 5 p.m. [35]. The American University of Sharjah's Institutional Review Board authorized the study's protocol (Protocol Code 19-513, date of approval 31 March 2020), which was created in accordance with the Helsinki Declaration.

B. Mental Stress Task
The SCWT was used as a stressor. It is based on monitoring six different color words in a random sequence (' ', ' ', ' ', ' ', ' ', and ' '). The displayed word on the computer screen was printed in a different color than the meaning of the word, and the correct response is the color of the typed word (for example, the word is written in yellow, therefore the correct answer is yellow word). In this incongruent and semantic example, subjects were supposed to call the ink color rather than reading the word. Hence, participants experienced this conflicting mental state by doing a less automatic activity (identifying the font color) while concealing the doubt generated by a more automated one (naming the word) [36].
In details, the SCWT was presented in two different phases: vigilance phase and stress phase. The Vigilance phase included a slow presentation for the SCWT questions and trials in which the respondent needed to reply as fast as possible but without time limit. The recorded average time in answering the SCWT questions during the vigilance phase was lowered by 20% in the stress phase which is utilized to exert time pressure on the subjects. The SCWT was created and tracked using MATLAB (R2020b, Natick, MA, USA). Failure to answer or replying wrong within the allotted time would result in feedback to the participants on their performance, such as "Correct," "Incorrect," or "Time is out". Therefore, a dummy user performance indicator was displayed with each trial, suggesting poor performance by the participants in comparison to their peers. Consequently, while completing the SCWT, behavioral data such as detection accuracy and average RT was gathered. This data was collected in order to determine the levels of stress. RT was measured as the average time it took from the onset of the SCWT to the time the participant clicks on the mouse key on the selected color displayed on the monitor. Meanwhile, the overall accuracy was calculated based on the number of the color word correctly matched over the total number of the displayed color word targets.

C. Salivary Alpha Amylase
Many studies have found a link between mental stress and salivary alpha amylase (SAA) levels [37], [38]. Catecholamines are present in salivary alpha amylase, with epinephrine and norepinephrine being the two most important neurotransmitters. While epinephrine has slightly more of an effect on the heart, norepinephrine has more of an effect on the blood vessels. During the fight or flight response, epinephrine and norepinephrine are released into the circulation and saliva. This release generates a quantifiable quantity that can be extracted from SAA samples [37]. According to Chatterton et al. [37], SAA concentrations predict plasma catecholamine levels and can be used as a stress indicator. Meanwhile, Rohleder et al. [38] showed that when individuals were exposed to Trier Social Stress Test, their SAA levels rose and then decreased after waking.
The amylase activity was measured using a hand-held monitor (COCORO meter, NIPRO, Osaka, Japan). Saliva was collected by dipping a salivary-sampling strip in saliva and placing it under the tongue for 40 seconds. The strip was then immediately placed in an automated saliva transfer system, where it was compressed and converted into alpha-amylase test paper. The salivary intensity reading was then computed, and the level of stress was determined. We collected salivary alpha-amylase samples to test if the SCWT has generated stress for all participants and to check the stress mitigation after applying 16 Hz BBs.

D. Data Acquisition and Pre-Processing
During the experiment sessions, brain activity was measured using an fNIRS system (NIRSport2, NIRx Medical Technologies, NY, USA) with 20 channels, 8 sources and 7 detectors, that cover the frontal cortex. The infrared signal was produced at two wavelengths, 760 nm and 850 nm, with a sampling rate of 10.17 Hz.
The experiment settings had a well-controlled environment with consistent temperatures and lighting conditions. Fig. 1 shows the experiment protocol, the SCWT procedure and the experiment setup. At the beginning of the experiment, participants were encouraged to carefully read a word file consisting of an introduction and explicit instructions on how to complete the task. This experiment was completed in five main sessions/phases, which are presented in blue squares in Fig. 1(a). Subjects did the SCWT for 10 minutes without fNIRS recording in the first phase, and feedback on performance was provided upon completion. fNIRS was acquired during the second phase, the Vigilance phase, while participants performed a 10-minutes Stroop task that consisted of 10 blocks/trials of questions of 30 seconds each, separated by resting periods of 20 seconds, as shown in Fig. 1(b). During Vigilance phase, participants were instructed to respond as quickly and accurately as possible, without any time limit per question. In the third session, or Enhancement phase, participants were instructed to utilize the headphones to listen to the 16 Hz binaural beats while solving the SCWT questions similar to the one presented in the Vigilance phase. Following that, the Vigilance phase's average time to answer each question was decreased by 20% and used as a time constrain for the Stress phase. As a consequence, the fourth phase, the Stress phase, was structured similarly to the Vigilance phase, with 10 minutes of recording time, but with restricted time per question. In the fifth phase, the Mitigation phase, participants were asked to use the headphones to have binaural beats stimulation while repeating the Stress phase. The last four SCWT phases were presented randomly, with half of the participants starting without audio stimulation and the other half started with audio stimulation. SAA sample was collected after each phase, resulting in five SAA samples per subject. The entire time for each participant, including introduction, preparation, and recording, was roughly one hour.
The MATLAB NIRS Brain AnalyzIR ToolBox was used to extract the fNIRS data and translate it into a change in optical density [39]. The concentration variations of the oxygenated hemoglobin (HbO) and deoxygenated hemoglobin (HbR) were then determined using Beer-Lambert law [40]. For movement artifact correction of sharp peaking signals, we employed temporal derivative distribution repair and Principal Component Analysis (PCA). To lessen the physiological noise induced by heart activity and breathing, a band-pass filter between 0.01Hz and 0.3Hz was used. In the baseline correction, we first defined a period from the onset to the end period of SCWT, lasting 30 seconds, as one single analysis block. Then, each block of the SCWT was baseline-corrected by subtracting the average value of the pre-task period, i.e., in the resting condition.

E. Functional Connectivity
PDC was applied on the pre-processed data to estimate the time-dependent multivariate auto regressive coefficients that describe the information flow between fNIRS signals. More details about the PDC and the model order, which was set to 6 using Akaike information criterion can be found in our previous studies [41], [42]. The frequency domain had 30 frequency bands between 0.01Hz and 0.3Hz with step size of 0.01Hz. The PDC matrix data format was 4 × 30 × 10 × 30 × 20 × 20, for experiment conditions × subjects × blocks of questions × frequencies × channels × channels. The PDC had a value between 0 and 1, with larger values indicating greater interaction between the two nodes.
We then developed an automated thresholding method for defining the presence of a connection between brain nodes. Similar to the previous Alzheimer study [16], we used a data-driven thresholding approach based on maximizing of global cost efficiency in order to save the most relevant connections from the full-weighted network and show the brain network's backbone. Global cost efficiency is defined in equation (1): where E g denotes the global efficiency of the brain functional network, which is used to quantify the network's capacity for information processing and transmission. P SW is defined as the ratio of existing edges divided by the total number of possible edges. We searched for the optimum threshold that maximizes the GCE by iterating the absolute values between (0-1, with step size of 0.01). d i j is the short path length and N is the number of nodes [43].

F. Graph Theory Analysis and Laterality Index
GTA offers quantitative measures for analyzing the topological architecture of functional connectivity networks. There are N nodes and W weighted edges in a specified network or graph G; the graph theory analysis produces global and local network metrics. In our research, the nodes are channels, and the connections are determined by the PDC connectivity metric. The brain network parameters are calculated based on the matrices generated by the PDC for each individual. The graphical analytic measures in this study are based on the notions of node degree, clustering coefficient, modularity and efficiency. The definitions and mathematical expression of these metrics can be found in our previous studies [41], [42].
To measure hemisphere dominance in the four mental states, the LI was used. Using equation 2, we found the LI for each GTA measure and for the PDC between the channels of the right hemisphere (R) and left hemisphere (L). The value of the laterality index lied between −1 and +1 where a positive value indicated right-hemisphere dominance and a negative value showed left-hemisphere dominance.

G. Statistical Analysis
This study attempts to examine mental states with and without BBs, as well as the situations of high vigilance and stress. Therefore, a statistical analysis was carried out between the Vigilance and Stress phases, as well as between those phases and their respective BBs phases (Vigilance/Enhancement and Stress/Mitigation). We employed two sample t-test, using Bonferroni-Holm correction method, to assess the connection metrics between Stress and Mitigation. Before conducting the statistical analysis, we used the Kolmogorov-Smirnov method to test the normal distribution of the data. Then, we first studied the behavioral data and alpha amylase levels by examining each of the SCWT's two phases concurrently. Second, we examined the connectivity measures nodal degree, clustering coefficients, modularity, and efficiency across Vigilance and Stress levels. Thirdly, we compared the connectivity metrics in nodal degree, clustering coefficients, modularity, and efficiency between the Vigilance and Enhancement phases, as well as the Stress and Mitigation phases. If the test rejects the hypothesis at the 5% level of significance, the result h is 1, otherwise it is 0. Finally, to determine hemisphere dominance in the four mental states, we calculated the LI for each graph theoretical analysis measure and the PDC between the right and left hemispheres' channels.

III. RESULTS AND ANALYSIS A. Salaivary Alpha Amylase Analysis
Each subject had five SAA samples taken throughout the entire experiment. Fig. 2 depicts the results of these samples, which were obtained five minutes before the experiment and immediately after the Vigilance, Enhancement, Stress, and Mitigation phases. The level of SAA increased from the Baseline to Vigilance phase by 227.83% and from the Vigilance to Stress phase by 32.09%, demonstrating that the SCWT with time pressure and negative feedback elicited level of mental stress. In contrast, the phases containing BBs, which are Enhancement and Mitigation phases, exhibited decreased amylase levels by 40.29% and 30.29% comparing to the Vigilance and Stress phases respectively. To determine the significant differences between the phases, a two sample t-test was used. Comparing the Baseline phase (the phase with alpha amylase sample prior to the experiment), the Vigilance and Stress phases demonstrated a statistically significant increase in the SAA level ( p < 0.001). This indicates the SCWT's stress-inducing capability. Meanwhile, the ability of BBs to enhance vigilance and alleviate stress was linked to the significant decrease in the alpha amylase level with p < 0.001 and p < 0.01 respectively.

B. Beahvioural Data
The behavioral data was collected throughout the four phases of experiment for the 30 subjects. As shown in Fig. 3a, the mean accuracy for answering the SCWT questions was 94.99%, 95.96%, 60.52%, and 71.57% for the Vigilance, Enhancement, Stress, and Mitigation phases, respectively. The two-sample t-test and Kruskal Wallis test between the Vigilance and Enhancement phases showed no significant difference in performance, no effect for the BBs on enhancing vigilance with p = 0.126. In contrast, statistical analysis between the Stress and Mitigation phases showed significant performance improvement under the BBs condition ( p < 0.001). Also, the difference between the accuracies scored under the Vigilance and Stress phases were notable with a significant decrease in answering accuracy ( p < 0.001). This revealed that the SCWT used in conjunction with time pressure and negative feedback was effective in raising stress levels. As a result, there was evidence that BBs improved the behavioral performance in the form of properly answering questions by 21.83% between Stress and Mitigation phases. Similarly, the applied statistical analysis showed a significant role for the BBs on reducing the RT to stimuli from Vigilance to Enhancement and from Stress to Mitigation as illustrated in Fig. 3b.

C. fNIRS Connectivty Analysis
Partial Directed Coherence was used to estimate the functional connectivity networks in the four mental states. As mentioned in the subsection (II-E), the PDC matrix had 6 dimensions and to get the adjacency matrix for each phase, the PDCs resulted from the post-processed fNIRS signals were subsequently averaged channel by channel across thirty frequency bands (0.01-0.3 Hz in step of 0.01) and for all the 30 subjects to get one PDC map for each phase as shown in Fig. 4. Hence, the size of the final PDC matrix was reduced to 3 dimensions (4 × 20 × 20) representing the experiment phases, fNIRS channels and fNIRS channels respectively. Each PDC node denotes the intersection of a sender fNIRS channel (the 20 channels on the x-axis) and a receiver fNIRS channel (the 20 channels on the y-axis) and vice vera. Decreases and increases in connectivity were shown in several channels corresponding to brain regions. The PDC drop suggested a loss of functional connectivity between frontal brain regions. Similarly, an increase in the PDC suggested an increase in the frontal brain network connectivity. For instance, channel 10 (right dorsolateral PFC) showed high impact in sending information in the stress phase, whereas no such impact was seen in receiving the information (Fig. 4a). Likewise, channel 19 (right ventrolateral PFC) had high effect in sending information to other frontal regions during the Vigilance phase (Fig. 4b) and Mitigation phase (Fig. 4d).
Following that, for each couple of SCWT phases (Vigilance vs Enhancement, Stress vs Mitigation, Vigilance vs Stress), a PDC connectivity map was constructed by subtracting the PDC maps. Examining these maps provided a clear explanation for the increase or decrease in information flow. In addition, a twosample t-test, using Bonferroni-Holm correction, was used to determine the significance of the PDC network nodes under varying levels of stress (p<0.0167). Each PDC node represents the intersection of a sender fNIRS channel and a receiver fNIRS channel. Based on that, Fig. 5 illustrates the significant difference in the connectivity networks between each two phases where the blue color represents high functional connectivity for the first phase under investigation and the red color represents high connectivity for the second phase. According to Fig. 5a, the results of BBs showed improved connectivity for right dorsolateral (channel 18) and right frontopolar (channel 14) prefrontal cortex. As seen in Fig. 5b, channel 18 in the right dorsolateral cortex had improved connectivity after applying BBs on high stress level situations. However, the Stress phase showed increased information flow in the left orbitofrontal prefrontal cortex (channel 11) at the expense of Vigilance phase (Fig. 5c). Fig. 6 illustrates the four main areas of the prefrontal cortex.

D. Graph Theory Analysis
The scalp maps for the full-scale nodal degree, clustering coefficients, modularity, and efficiency are shown in Fig. 7. The mapped values are the overall average of all subjects. A two-sample t-test ( p < 0.0167) was used for each channel to evaluate its statistical significance in the local topology between the phases Vigilance and Enhancement (Fig. 7a), Stress and Mitigation (Fig. 7b) and Vigilance and Stress (Fig. 7c). All channels that demonstrated significant differences between the Vigilance and Enhancement phases (Fig. 7a) had a negative t-value. This confirmed that GTA measurements (clustering coefficient and network efficiency) had increased in value throughout the right orbitofrontal PFC (channel 13). Similarly, negative t-values were found for all significant channels throughout the entire GTA measurements between the Vigilance and Stress phases across varied brain regions (Fig.7c). In contrast, right dorsolateral PFC, with a significant role between Stress and Mitigation phases (Fig. 7b), showed positive t-values that are correlated to decreased network efficiency.

E. Laterality Index
The findings of the laterality index (LI) characterized the dominant hemisphere across the four mental states. Fig. 8 compares the regional LIs of the nodal degree, clustering coefficients, modularity, efficiency and PDC under Vigilance, Enhancement, Stress and Mitigation phases. The mean LI values are shown together with error bars reflecting the standard error across subjects. Asterisks ( * ) indicate a statistically significant difference in the LI between the two   hemispheres, where positive values denote right lateralization, while negative values denote left lateralization. The statistical analysis ( p < 0.0167) indicated a significant difference between the channels of the orbitofrontal cortex (4 → 19, 13 → 11) for most of the graph theoretical analysis measures and PDC. However, only in the Enhancement phase did the dorsolateral region show substantial differences between the two hemispheres. Likewise, the Enhancement phase had the majority of significant differences, whereas the Mitigation phase showed the minority of significant differences between the two hemispheres.

F. Relationship Between Functional Connectivity and Behavioral Response
In this part of the experiment, we compared the changes in connectivity degree, called nodal degree, with the accuracy of detection across the four phases/mental states. To begin, we calculated the changes in nodal degrees between each two phases by subtracting the Vigilance group's nodal degree from the Enhancement group's nodal degree, the Stress group's nodal degree from the Mitigation group's nodal degree, and lastly, the Vigilance group's nodal degree from the Stress group's nodal degree. These subtraction operations were based on the one-versus-all principle. In this case, the average nodal degree of each subject in the vigilance group may be deducted from the average nodal degree of all other individuals in the enhancement group. The ultimate nodal degree was then calculated using the weighted sum. Positive nodal degree difference implied network enhancement, whereas negative degree indicated network impairments or decline. Second, identical to what was said previously, we determined the variations in SCWT accuracy by subtracting the recorded accuracy between each two phases. A positive difference in accuracy implied an improvement, whereas a negative difference suggested an impairment. As shown in Figures 9a and 9b, changes in nodal degree were mildly negatively correlated with SCWT accuracy throughout the phases with and without BBs, although a positive correlation was observed between the Vigilance and Stress phases (Fig. 9c).

IV. DISCUSSION
In this study, we examined two significant stress-related issues that are prevalent in a range of operational and industrial contexts. First, a quantitative method to assess stress was suggested based on graph theory analysis of automated fNIRS directed functional connectivity. Second, the efficacy of auditory stimulation in improving vigilance performance and mitigating stress was examined. To the best of our knowledge, this is the first fNIRS study to automate the directed functional connectivity network using the GCE with PDC as well as to investigate the effectiveness of BBs on vigilance and stress levels at the same time.
We found that performing SCWT under time pressure and negative feedback significantly influenced the performance, owing to the high cognitive load necessary to maintain attention to the task. Hence, there was a significant decline in behavioral responses in the Stress phase. The accuracy of detecting SCWT stimuli decreased by 36.3%, 36.9% and 18.3% in the Stress phase compared to each of the Vigilance, Enhancement and Mitigation phases, respectively. Stress caused a loss in response accuracy and a rise in RT to stimuli, while the use of BBs during the Enhancement and Mitigation phases was associated with an apparent improvement in response accuracy and a decrease in RT. Consistent with our earlier EEG work on vigilance decrement [42], the considerable increase in RT indicates a genuine drop in accuracy for timely response rather than a speed-accuracy tradeoff [44]. Additionally, using alpha amylase as a reference, we confirmed that the applied time constrain significantly increased the stress level for all participants ( p < 0.001) when compared to the Baseline and Vigilance phases. As shown in Fig. 2, the significant increase in salivary amylase levels was related with the phases that did not involve BBs, whereas the significant drop was linked with the phases that included BBs and the Baseline phase. This confirms that the SCWT induces significant levels of stress, and that the BBs have a good impact on increasing vigilance and reducing stress.
We also found that the connectivity of the right prefrontal cortex diminished with stress as illustrated in Fig. 4c and Fig. 5c. It has previously been shown that the right prefrontal cortex is the most susceptible brain region to mental stress, which can be seen by decreased HbO levels under stress circumstances [45]. Likewise, mental stress reduced the flow of information from the right to the left hemisphere. The lack of attentiveness in this area might be a sign of a decline in spatial engagement, which in turn could lead to a drop in response accuracy. Thus, the brain network in Fig. 5c confirms that, when the degree of stress rises, the flow of information in the right prefrontal cortex decreases. Meanwhile, the effectiveness of BBs demonstrated a major influence in reducing stress in the right dorsolateral PFC, particularly channel #18, as well as a considerable effect on enchanting alertness over most of the PFC. Activation of the auditory primary area in the cortex could be responsible for the increase in connectivity networks between the right hemisphere and dorsolateral prefrontal cortex. Previous research has shown that BBs stimulation increases the capacity of auditory cortical areas to exchange information [46], [47]. As well, Al-Shargie et al [48] revealed that listening to 16 Hz binaural beat stimulation during high vigilance improved behavioral performance and reduced stress levels in the participants. In contrast to study [48], which estimated the network's connectivity using an undirected technique, this study employs directed connectivity to provide insights on the probable brain activity mechanism in directing life activities.
Our results of the nodal degree, clustering coefficients, modularity and efficiency were significant for certain channels, or brain regions, throughout the Enhancement and Mitigation phases. BBs increased connectivity between the right ventrolateral and right dorsolateral prefrontal cortices during highvigilance SCWT performance. In the meanwhile, a restricted right frontopolar area had diminished connectivity. After applying BBs to high-stress situations, the right prefrontal cortex's connectivity was enhanced. To the detriment of the Vigilance phase, the Stress phase enhanced information flow in the left orbitofrontal prefrontal cortex. While conducting the SCWT and listening to the auditory stimulation, the increased connectivity between brain areas showed improvement in the overall information processing that may represent a mood of excitement. One potential explanation is that multimodal stimulation helped to alleviate tension and improved sustained attention. Another interpretation is that the enhanced connectivity with generated stress was caused by participants' heightened compensatory attempt to maintain attention for stimulus onset.
As illustrated in Fig. 8a, the network in the orbitofrontal prefrontal cortex exhibited a statistically significant rightward density shift throughout all task phases. Likewise, asymmetric functional segregation was only detectable in the dorsolateral and orbitofrontal prefrontal cortex under the Enhancement and Stress phases respectively (Fig. 8b). In the Enhancement phase, the dorsolateral and orbitofrontal PFCs demonstrated statistically substantial rightward functional integration within the local efficiency. According to Fig. 8e, the orbitofrontal PFC maintained statistically significant rightward information flow throughout the four stages.
The enhanced vigilance for the dorsolateral and left ventrolateral prefrontal cortex, as well as the alleviated stress for the right dorsolateral prefrontal cortex, had the greatest impact on local efficiency when comparing the connectivity network between phases without BBs (Vigilance & Stress) and phases with BBs (Enhancement & Mitigation). Findings showed an increase in connectivity patterns on the right side of the brain. These results reported that auditory stimulation could be an effective method of reducing mental stress in work environments that require prolonged concentration. Similar articles described state-of-the-art methods for cognitive enhancement. Therefore, Table I compares the outcomes depicted in the literature following the application of BBs.
Correlating the findings of the GTA with behavioral data revealed an inverse relationship between target detection accuracy and nodal degree for the enhanced vigilance condition. However, no correlation was found between the nodal degree and the accuracy of target detection under stress when listening to BBs. In contrast, a direct effect was established between high vigilance and high stress levels.  AND SUGGESTED FUTURE WORK The purpose of this study was to determine the effect of Binaural Beats stimulation on enhancing vigilance and reducing stress. In scenarios requiring mental state discrimination, the PDC has been proven to be one of the most effective estimators of anticipated functional connectivity. However, because we captured only the frontal region, we can consider high density fNIRS to simultaneously investigate all potential cortical neuronal networks. Using a pulse oximeter and a short-distance measurement simultaneously could significantly minimize the scalp effect and systemic noise [54]. While we explored BBs at a single frequency of 16 Hz in this study, future research should investigate more frequencies.
The sample size was adequate, however future research should take into account the gender discrepancy. On the other hand, utilizing a multimodal neuroimaging approach would be useful to quantify both mental stress and the effect of BBs on stress reduction.
VI. CONCLUSION This study investigated the impact of auditory stimulation on cognitive vigilance and mental stress in the workplace. We developed an experiment to induce stress by subjecting participants to the SCWT under time constraints and negative feedback. Then, we employed 16 Hz BBs to promote attentiveness and decrease stress. We found that listening to 16 Hz BBs for 10 minutes enhanced mental states by significantly enhancing the target detection accuracy by 21.83% ( p < 0.001) and decreasing the salivary alpha amylase levels by 30.28% ( p < 0.01). Besides, we found a significant decrease in the information flow from left to the right PFC during stressful situations. Meanwhile, the use of 16-Hz BBs increased the connectivity in the dorsolateral and left ventrolateral prefrontal cortex.