# A Novel Approach for Acute Mental Stress Mitigation Through Adapted Binaural Beats: A Pilot Study
## 3 Results  
As mentioned in Section 2.3, the data collected in steps 1 and 2 (see Figure 1B) were used to train the regressor. Participants showing an average coefficient of determination (\(R^{2}\)) lower than 50% during cross-validation were excluded, along with those not simultaneously showing an increase in heart rate during steps STIM ON compared to STIM OFF (see Figure 1B) and a level of perceived stress estimated through the VAS lower than three, thus indicating that the tasks were not perceived as sufficiently stressful. Additionally, one subject was excluded due to technical issues after the training. Overall, a total of 13 subjects were considered for the subsequent analysis. For those participants, the results of the questionnaires, indicated as mean \(\pm\) standard deviation, were 22.08 \(\pm\) 6.99 for the PSS, 37.54 \(\pm\) 9.86 for the STAI, and 57.69 \(\pm\) 9.38 for the NASA-TLX. Considering the ranges reported in [45] for the FSS (i.e., low: [0-13], moderate: [14-26], and high [25-40]) and the ones in [46] for the STAI (i.e., low: [20-37], moderate: [38-44], and high: [45-80]), the mean values of the self-report assessment indicate moderate stress and state anxiety before the beginning of the experiment. On the other hand, the results of the NASA-TLX suggest that participants experienced a high mental workload because of the experiment [17]. The stress index trends for all the participants during training are shown in Figure 3A. The purple block includes the predictions during the VID, whereas the remaining is relative to the MAT. Overall, regressors showed an average \(R^{2}\) of 0.78 during the training phase. In addition to the stress index, the average heart rates during the tasks and the results of the VAS are shown in Figure 3B,C, respectively. For the latter plots, the median values of the two distributions are reported. The results indicate statistically significant differences (\(p<0.01\)) between the VID and MAT. Figure 4A illustrates the regressor's feature ranking, where the average importance of each feature is reported. The \(RR\) interval finds the first place in the ranking with an average importance of about 50%. Despite the general trend, this was not valid for all the participants. Indeed, Figure 4B,E show the top five features of two participants, and the \(RR\) was not always in first place. Figure 4C,F depict the boxplots of the \(RR\) intervals during the two tasks, whereas 4D,G are relative to \(RT_{R}\). Despite the statistically significant differences between the VID and MAT's distributions (not represented in Figure 4), it is possible to appreciate differences in the overlap of the boxplots, which can be quantified through the area under curve (AUC) of the receiver operating characteristic. For the first subject (Figure 4C,D), the \(AUC\) was higher for the \(RR\) interval rather than the \(RT_{R}\). On the other hand, an opposite result can be appreciated for the second subject (Figure 4F,G), with a higher \(AUC\) for \(RT_{R}\) than the \(RR\) interval. The stress predictor (5) changes over time are reported in Figure 5A,B. The figures take into account the two possible stimulation orders: adapted stimulation followed by a constant one (AC) and vice versa (CA). The purple block represents predictions during the VIDs (STIM OFF), whereas the yellow and light orange blocks correspond to adaptive (ABB) and constant (CBB) stimulation (STIM ON), respectively. For both Figure 5A,B, the participant stress predictor is reported in gray, whereas the black line represents the average of the curves. Regardless of the stimulation order, ABBs showed lower mean values of \(S\): 0.69 (ABB) and 0.76 (CBB) for AC, and 0.68 (CBB) and 0.59 (ABB) for CA. Ultimately, Figure 5C shows the \(f_{BB}\) frequencies over time for the ABB condition. Figure 3: (**A**) Stress index trends during steps 1 and 2 (training phase) for all the participants. The solid black line represents the average of the curves. Results indicate an average determination coefficient (\(R^{2}\)) of 0.78.