Alpha neurofeedback has a positive effect for participants who are unable to sustain their alpha activity.

Alpha rhythm (8-13 Hz) is linked to relaxed mental state in humans. Earlier reports have shown that individuals can increase their alpha power if provided with a valid feedback, compared to controls who are provided invalid feedback. However, these results remain controversial, partly because controls may be in a different behavioural state, making it difficult to directly compare their alpha power with the valid group. We here address this issue by using an experimental paradigm in which an invalid feedback is given on a fraction of trials, such that both valid and invalid conditions can be obtained from the same participant. Using EEG, we recorded alpha power from the occipital area from 24 humans (9 females) and played a feedback tone which could be valid (tone frequency proportional to alpha power), invalid (tone sequence from a previous valid trial; participants were unaware of this condition), or neutral (constant tone frequency). We found that during eyes closed-state, neurofeedback did not enhance alpha activity beyond pre-trained state within the experimental duration, probably because of saturation of alpha rhythmicity. However, for participants whose alpha power decreased over time within a trial, valid feedback helped them to sustain alpha more than invalid feedback. Further, alpha increase showed a weak negative correlation with their self-reported attentional load but was uncorrelated with relaxation levels. Our results reconcile many conflicting reports in the neurofeedback literature, and show that even under most stringent control, valid neurofeedback can help participants who are otherwise unable to sustain their alpha activity.Significance Statement We tested whether providing a real time auditory feedback about the strength of the EEG alpha rhythm helps the participants increase their alpha power. Unlike previous neurofeedback studies that used valid and invalid feedback on different participant groups, we used a design in which valid, invalid and neutral feedback were given to the same participant. We found that for participants whose alpha power reduced over time within a trial, valid feedback helped to sustain the rhythm better than invalid feedback. Further, feedback appeared to be more useful for participants who did not attend the tone. These findings can be used to better screen and design neurofeedback training paradigm, which is now used to treat patients suffering from anxiety and depression.


Introduction
In EEG signals, a brain rhythm in the frequency range between 8 and 13 Hz, called alpha, is prominently ob-served in the occipital area of many individuals, especially during an awake and relaxed state with eyes closed (Berger, 1929;Adrian and Matthews, 1934). Although alpha was traditionally believed to be an idling rhythm, recent studies have linked alpha rhythm with high-level cognitive mechanisms such as attention (Kelly et al., 2006a;Klimesch et al., 2007), information retrieval (Klimesch, 2012), and creativity (Fink and Benedek, 2014). Therefore, it has been suggested that learning to control the alpha activity may have a positive effect on the mental state (Escolano et al., 2011;Zoefel et al., 2011;Klimesch, 2012;Nan et al., 2012).
Alpha Neurofeedback involves providing individuals a real-time feedback about their alpha power (Kamiya, 1969(Kamiya, , 2011, which is typically provided by a tone (Kamiya, 1969;Plotkin, 1978;Dempster and Vernon, 2009;van Boxtel et al., 2012), or occasionally by a visual signal (Brown, 1970;Dempster and Vernon, 2009;Ros et al., 2010Ros et al., , 2013. Early neurofeedback studies reported that participants could learn to enhance their alpha activity with the aid of neurofeedback training (Kamiya, 1969;Brown, 1970;Nowlis and Kamiya, 1970;Hord and Barber, 1971;Hardt and Kamiya, 1976), which could further have a beneficial effect on their behavioral state, such as reduction in anxiety (Garrett and Silver, 1976;Hardt and Kamiya, 1978) or sleep need (Regestein et al., 1973). However, these findings were subsequently challenged, because the constitutional, physiological and cognitiveattentional state of the participant could vary during training, and that itself could change alpha power (for review, see Lynch and Paskewitz, 1971;Plotkin and Rice, 1981;Rice and Blanchard, 1982). For example, participants may be anxious/attentive during the beginning because of an unfamiliar setting and may get more relaxed during the training. This alone could increase alpha power over time, irrespective of feedback.
One way to address this concern is to have a "control" group to which invalid or no feedback is provided. Early studies that employed such controls gave conflicting results, with some studies showing an increase in alpha even with no/invalid feedback (Strayer et al., 1973;Lynch et al., 1974;Lindholm and Lowry, 1978), while others showing no increase without valid feedback (Beatty, 1971(Beatty, , 1972. Some studies attributed this discrepancy to methodological differences (Paskewitz and Orne, 1973;Walsh, 1974;Hardt and Kamiya, 1976;Ancoli and Kamiya, 1978;Vernon et al., 2009). Others have suggested that even this design is not sufficient (Rogala et al., 2016;Biswas and Ray, 2017), since the behavioral state of the control and contingent groups may be different. For example, the control group may stop paying attention to the feedback if they realize that it is not helping them. Further, small effects may not be observed due to large interparticipant variability in alpha power across the contingent and control groups (Haegens et al., 2014). To address these concerns, a design is needed in which each participant could potentially be his/her own control (Biswas and Ray, 2017).
To address this, we designed an experiment in which we provided invalid feedback (representing alpha activity from a trial in a previous block) to the participants in 25% of trials, along with valid (50%) and no feedback (25%). The participants were completely unaware about the invalid trials, and therefore the behavioral conditions (for example, amount of attention paid to the feedback tone) were identical to the valid case. We then investigated whether valid feedback had a stronger effect on alpha power than invalid feedback. Further, in our design the participants were free to either use or ignore the feedback, which allowed us to study the correlation between enhancement of alpha power with subjective attention and relaxation levels, which participants provided after the task.

Participants
Twenty-four healthy volunteers (mean age: 23.9 years, females: 9) participated in the study. The protocol used for EEG recording was approved by the Institutional Human Ethics Committee of the Indian Institute of Science (IISc). Before conducting the experiment, the participants were briefed about the experimental procedures (see Experimental paradigm) and the risks involved, after which written informed consent was obtained. Participants were requested to sit comfortably in front of a computer monitor and to avoid any unnecessary movements during the experiment.

Experimental paradigm
The experiment was divided into five sessions. Each session consisted of a calibration stage (15 s), followed by 12 trials of 50 s each (Fig. 1A). There were three types of trials: valid, invalid, and neutral/constant. During valid trials, the frequency of the feedback tone was directly proportional to the change in alpha power from baseline (computed during the calibration phase). During invalid trials, which were presented from the second session onwards, one of the valid trials from the first session was chosen and the tone sequence for that session was presented. For constant trials, the frequency of the feedback tone was kept constant throughout the trial. The first session (termed "pre-training" phase because the subjects were naive to the task) consisted of three constant and nine valid trials. From the second session onwards, three invalid trials were presented in each session, along with three constant and six valid trials. The participants were not informed about the invalid trials, so for them, the trial composition was 25% constant and 75% valid for each of the five sessions (the actual composition from second session onwards was 50% valid, 25% invalid, and 25% constant). The entire trial sequence was generated This work was supported by Wellcome Trust/DBT India Alliance (500145/Z/ 09/Z; Intermediate fellowship to S.R.), Tata Trusts grant, and the Department of Biotechnology-Indian Institute of Science (DBT-IISc) Partnership Programme.
pseudo-randomly for each participant at the beginning of the experiment. Note that the first session was not used for analysis because it had no invalid trials and the participants were getting accustomed to the task during this session. However, including the first session data for the analysis yielded very similar results (data not shown).
Each session started with a calibration process, in which participants were asked to keep their eyes open without blinking. The calibration process yielded a "baseline" value of the alpha power (average alpha power between 6 and 15 s), which was used for calibrating the pitch of the feedback tone for that session. The calibration process was occasionally repeated if the participants blinked or there was any movement artifact (assessed by manual inspection of the time-frequency spectrum of the EEG signal that showed a broadband response due to such artifacts), although this happened rarely. We did not implement any online artifact rejection. During the neurofeedback training, participants had their eyes closed, so no significant artifacts were observed related to eye movement/blink.
During each trial, for the first 15 s, participants were asked to keep their eyes open. From 6th second onwards, a tone was played whose frequency was modulated in three different ways depending on the trial type, as de-scribed above. Fifteen seconds after the trial onset, a message was displayed on the monitor screen instructing participants to close their eyes and relax as much as possible. The participants were instructed to try to maximize a "performance score," which reflected the average change in alpha power from the baseline power (measured during calibration time) in the interval between 21 and 50 s after trial onset and was displayed at the end of the trial on the monitor screen. This score reflected the true change in power, irrespective of the trial type. Once the trial ended, the tone stopped, and the experimenter asked the participant to open his/her eyes and view their performance score. There was no fixed inter-trial interval; the participants simply indicated by a hand gesture to the experimenter whenever they wanted to start the next trial. The total duration of the experiment was ϳ1.5 h.
Importantly, participants were told that the pitch of the feedback tone in non-constant trials was proportional to the relaxation score, but they were not instructed to explicitly pay attention to the feedback tone. Specifically, they were told that they had the liberty to use the feedback tone to improve performance but could also ignore the feedback tone if they felt it was distracting and was not aiding them in increasing the performance score. Indeed, different participants used different strategies, as revealed by their responses to a questionnaire presented at the completion of all the sessions.

Questionnaire
After the experiment, all the participants were required to fill up a questionnaire consisting of the following four questions. (1) Was the task relaxing? (relaxation score: 1, not at all relaxing; 10, very relaxing). (2) Was the tone acting as a source of disturbance? (distraction score: 1, not disturbing; 10, very disturbing). (3) Were you using the feedback provided by the tone? (attention score: 1, ignored the tone completely; 10, paid attention to the tone as much as possible). (4) Which method or technique were you using to relax?
Because we asked the participants to fill out the questionnaire only at the end of the experiment, this single evaluation might have been biased by the most recent and vivid experience of the last session only. This issue could have been partially addressed if we had asked them to provide a response at the end of each session (or even perhaps each trial). However, answering questions after each session could have disrupted the continuity of the training/learning and would have increased the duration of the study. Also, we were more interested in the overall effect of neurofeedback that was experienced for the entire duration of the study.

EEG setup and data acquisition
EEG signals were recorded from all the participants using Brain Amp DC EEG acquisition system (Brain Amp DC, Brain Products GmbH). Five electrodes were placed on the occipital region (PO3, O1, O3, O2, PO4) following international 10 -20 standard reference scheme. FCz was used as a reference electrode. Impedance value was kept Ͻ10 k⍀ for all the electrodes. Raw EEG signal was sampled at 500 Hz, filtered between 0.016 Hz (first-order filter) and 250 Hz (fifth-order Butterworth filter) and was digitalized at 16-bit resolution (0.1 V/bit).

Real-time neurofeedback system design
The feedback system was developed using custom written codes in MATLAB (MathWorks Inc., RRID: SCR_001622) and standard socket programming. TCP/ UDP/IP MATLAB toolbox (version 2.0.6, GNU General Public License) function pnet was used to create a TCP/IP connection between the machine hosting MATLAB and the RDA server of Brain Vision Recorder, which is the proprietary software provided by Brain Products GmbH. Raw data were acquired from the RDA server via TCP/IP protocol into the system port where MATLAB was running. Once the number of data points in the port matched the sampling frequency at which EEG data were acquired by the Brain Vision Recorder (1 s of data), it was further processed in MATLAB for power estimation.
Power of this 1-s-long signal was estimated using multitaper method using a single taper, implemented in the Chronux package (Bokil et al., 2010), yielding a frequency resolution of 1 Hz. Power was first averaged across electrodes, and then averaged over the alpha range (8 -13 Hz) to get alpha power. Because the alpha power varied considerably over time, we took the average power over previous 5 s for generating the feedback tone (Fig. 1C, dotted line). Consequently, the feedback tone could be provided only from 6th second onwards. We calculated the change in alpha power as follows: where ⌬P ␣ denotes the change in alpha power in decibel calculated at time t; P e is the mean alpha power over a 5-s interval preceding t, and P c is the mean alpha power during the calibration period (taken only once per session). The frequency of the feedback tone (Fs, in Hz), played to the participants using a speaker located in front of them, was calculated according to the following equation: F s ͑t͒ ϭ 1000 ϩ ⌬P ␣ ͑t͒ ϫ 500 . (2) Note that for estimating alpha power, we did not bandpass filter the EEG data, but instead used multitaper method and averaged the power in the alpha band instead. Further, this analysis was performed separately at each second of data, and hence there was no overlap in the analysis windows (although we averaged power estimates over the previous 5 s for generating the feedback tone). Once the tone frequency was estimated (Eq. 2), the tone was generated for 1 s. The delay between subsequent feedback tone signals was limited to the computational time to perform these analyses once data were collected for that second. Behaviorally, successive feedback tones appeared almost instantaneously with no gap, suggesting that the computation time was negligible.

Statistical analysis
All statistical analyses were performed in MATLAB (MathWorks Inc.). One-sample two-tailed t test was used at significance level ␣ ϭ 0.05 to check whether the slopes of the regression lines were significantly different from zero. To check whether mean alpha power duirng valid trials was significnaly different compared to invalid trials, two-sample one-tailed t test was performed at the significance level ␣ ϭ 0.05 assuming unequal variances. Bonferroni correction was done to adjust the significance level to ␣ ϭ 0.0021 (0.05/24) whenever multiple comparisons across 24 participants were required.

Results
We recorded EEG (Brain Amp DC, Brain Products GmbH) from 24 healthy young adults using five active electrodes covering the occipital area. Figure 1A shows the experimental paradigm, which consisted of 60 trials of 50 s each, divided into five sessions. An auditory feedback was provided in each trial, which could be valid (red), invalid (green; given only from second session onwards), or a constant tone (blue). Figure 1B shows the change in time-frequency power (in dB) in one valid trial (trial 16), from a baseline power computed in a calibration stage just before the start of the session (in this case, before trial 13). Alpha Power was enhanced by Ͼ5 dB as soon as this participant closed eyes (16th second onwards) and remained high until the end of the trial (50th second). Figure 1C shows the change in alpha power over time, calculated by averaging the power in the alpha band (between the dotted black lines shown in Fig. 1B), which showed a transient peak at the 16th second just when the eyes were closed, and remained high thereafter. This change in alpha power was averaged over a 5-s window (dotted line) and used to set the frequency of the feedback tone (green trace). Figure 1D shows the alpha power for all trials for this participant, during eye closed (21-50 s after stimulus onset; filled triangles) and eye open (6 -15 s, open circles) states. The baseline power used for setting the feedback tone frequency (same value for each trial within a session) is shown by a black line, which was comparable to the alpha power during the eyes open state. To test whether feedback training enhanced alpha power over time, we performed linear regression analysis between alpha power and trial number (starting from session 2). For this subject, the slopes were not significant for either eye open or eye closed conditions (eyes open: slope ϭ 0.002 Ϯ 0.001, t (47) ϭ1.903, p ϭ 0.063; eyes closed: slope ϭ 0.002 Ϯ 0.002, t (47) ϭ 0.655, p ϭ 0.516). Results were similar when the analysis was restricted to trials of the same type (data not shown).
Across the population of 24 participants, the mean slopes of alpha power versus trial number were 0.002 Ϯ 0.0005 and 0.001 Ϯ 0.0006 for eyes open and eyes closed states, respectively. For eyes open condition, the mean slope was significantly different from zero (N ϭ 24, t (23) ϭ 2.936, p ϭ 0.007). However, the behavior of the participants was not well controlled during this condition; it is possible that they made different strategies during this phase early during the experimental session, which could have lowered their alpha power. Importantly, the slopes were not significantly different from zero (N ϭ 24, t (23) ϭ 1.594, p ϭ 0.125) during the eyes closed condition, during which their behavior was more controlled, and their alpha power was much higher than the eyes open condition. Therefore, during the eyes closed period, neurofeedback training did not significantly enhance alpha power over the entire course of the experiment.
To test whether the type of feedback had any effect on alpha power within a trial, we plotted the change in alpha power from baseline averaged over the three trial types (Fig. 1E). For all trial types, a peak was observed as soon as this participant closed the eyes (16th second), which may be the "alpha squeak" effect on eye closure (van Leeuwen et al., 1960). During the later period (after ϳ25 s), however, ␣ power decreased for the invalid and constant trials, but remained relatively more elevated for valid trials. To quantify this, we again performed linear regression analysis between change in alpha power and time between 21 and 50 s. For this subject, slopes were significantly negative for invalid and constant trials, but not for valid trials. Consequently, the average change in alpha power was about ϳ1 dB larger for valid as compared to invalid trials (7.43 vs ϳ6.47 dB). Note that although the invalid condition had the same stimulus statistics and presumably the same behavioral state as the valid one, the alpha power for invalid condition was actually more similar to the constant condition for which the tone was constant and uninformative. Figure 2 shows the same analysis as shown in Figure 1E for all 24 participants, sorted in decreasing order of significance of the difference in mean alpha power (averaged between 21 and 50 s) between valid and invalid conditions. The alpha power between valid and invalid conditions was significantly different for 11 (6 after Bonferroni correction for the number of participants) out of 24 participants, suggesting that the effect of neurofeedback was subtle and not applicable to all participants. Interestingly, like Figure 1E, alpha power in the invalid condition was similar to the constant condition for several subjects who showed a positive effect of neurofeedback, although the stimulus and behavioral aspects for invalid condition were matched to the valid condition. This suggests that the evolution of alpha power over time may actually depend on the "usefulness" or "information" provided by the feedback, since both invalid and constant trials were, on average, equally un-informative.
A closer look at Figure 2 revealed an interesting trend for the participants who showed a significant effect: for most of these participants, alpha power appeared to decrease over time, suggesting that these participants could not sustain their alpha rhythm. To quantify this effect, for each participant, we plotted the slope of alpha power versus time for the constant trials (Fig. 1E, blue line) versus the overall change in alpha power between the valid and invalid conditions (Fig. 3). Indeed, the participants who showed a significant increase in alpha power also tended to have negative slopes, and there was a strong negative correlation between the two variables (slope ϭ -7.668 Ϯ 1.591, t (23) ϭ -4.817, p ϭ 8.22 ϫ 10 Ϫ5 ). This suggests that neurofeedback mainly helped participants increase their alpha power who could not otherwise maintain their alpha activity.
Finally, we tested whether the change in alpha power was correlated with subjective experience (Fig. 4). Interestingly, we found a negative trend between change in power and how much participants paid attention to the feedback tone (slope ϭ -0.130 Ϯ 0.076, t (23) ϭ -1.703, p ϭ 0.103; Fig. 4A); the results failed to reach significance only because of one outlier participant who completely ignored the tone; removing this participant from analysis yielded a slope of -0.261 Ϯ 0.086, t (22) ϭ -3.036, p ϭ 0.006) suggesting that participants who were actively attending to the feedback tone did not benefit from neurofeedback. Indeed, the participants who had the strongest effect of neurofeedback (participants 1-6, filled black triangles) were the ones who were neither fully attending nor fully ignoring the tone. There was, however, no such trend between alpha power and the participant's selfreported level of relaxation (slope ϭ -0.127 Ϯ 0.189, t (23) ϭ -0.670, p ϭ 0.510; Fig. 4B) or whether they were disturbed by the tone (slope ϭ 0.077 Ϯ 0.080, t (23) ϭ 0.964, p ϭ 0.346; Fig. 4C). However, all the participants reported relaxation score of 5 and above (mean score, 7.958 Ϯ 0.213), indicating that they felt relaxed after the neurofeedback task (Fig. 4B).

Discussion
Using a novel design in which each participant was his/her own control, we tested whether participants were able to enhance their alpha power with valid neurofeedback more than false or no feedback. We found no enhancement of alpha power (during eyes closed state) over trials, although valid neurofeedback was provided during the major part of the experiment (33 out of the 60 trials; 50 s each). However, we found that in participants who could not sustain their alpha power, providing valid neurofeedback helped in sustaining alpha power within a trial more than when false or no feedback was provided. Surprisingly, participants who showed enhancement in alpha power with valid neurofeedback were the ones who did not pay too much attention to the neurofeedback tone. Overall, our results suggest that alpha neurofeedback, even when compared against a very stringent control condition, can help in the maintenance of the alpha power in some participants, and further recommend "passive attention" to the neurofeedback for best results.

Comparison with previous studies
Our results are consistent with earlier studies where alpha enhancement beyond pre-training levels was not observed (Lynch and Paskewitz, 1971;Paskewitz and Orne, 1973;Lynch et al., 1974;Walsh, 1974;Plotkin, 1978Plotkin, , 1979Cho et al., 2008;van Boxtel et al., 2012), and in contrast to studies which reported alpha enhancement (Hart, 1968;Kamiya, 1969;Brown, 1970). The temporal profile of alpha power, which tended to decrease with time, as well as the effect of neurofeedback, which helped to better maintain the power at elevated levels, are also in line with a previous study (Cho et al., 2008).
As discussed earlier, in our experimental design, the duration of feedback was short (50 s per trial), and valid feedback was inter-mixed with neutral and false feedback, to minimize the difference between valid and invalid conditions. We were especially concerned that prolonged invalid feedback might evoke a "surprise effect" because the feedback may be very different from what the participant may be feeling, or the participant may start ignoring the feedback if they realized that it was not valid or useful. Although such effects cannot be completely ruled out even in our design (in fact, in any neurofeedback design), having short duration of invalid feedback trials and intermixing these with a higher proportion of valid/neutral trials is likely to reduce these effects. Also, previous studies have typically used taped feedback from a different, control group of participants (Path et al., 1976;Watson and Herder, 1980;Hammond, 2005;Zoefel et al., 2011;Nan et al., 2012) or feedback based on a different frequency band (Egner et al., 2002;van Boxtel et al., 2012). The rate at which power varies in another individual or in a different frequency band is likely to be different, such that the statistics of the feedback signal (for example, how fast it varies with time) itself may be different across valid and invalid conditions, leading to a larger surprise effect. Further, it is possible that alpha power may depend on how the feedback tone varies over time (irrespective of the trial type), which may be different for valid versus invalid con-  Figure 1E, separately for each of the 24 participants, in descending order of significance of the difference between change in alpha power between valid and invalid trials (estimated using t test and shown in the plots, along with the mean changes in alpha power for the three trial types). ditions in previous studies. In our study, these confounds are largely ruled out because the invalid feedback tone was based on the subjects' own alpha power during a previous, valid trial. Therefore, the statistics of the tone signal was identical for valid versus invalid conditions. Indeed, when we asked the participants (after the completion of recording from all the participants) about the existence of the third (invalid) type of trials, all the participants who were reachable and remembered the experimental details (18 out of 24) were ignorant about the invalid trials (we did not ask the participants about the existence of the invalid trials immediately after their own recording because of the possibility of the interparticipant discussion about the experimental details). Figure 3. Effect of neurofeedback depends on sustenance of alpha power. Scatterplot shows difference in power between valid and invalid trials (⌬ power) and slope for the constant trials for all the 24 participants. Thick black line shows a regression line; slope and p values are indicated in the panel. Participants 1-6, for which mean change in alpha power between valid and invalid trials was significant after Bonferroni correction, are indicated using filled black triangles. Participants 7-11, for which the difference was significant before Bonferroni correction, are indicated using gray triangles. Remaining participants are indicated using open circles. Error bar indicates SEM. Further, keeping a short trial duration ensured that participants did not get drowsy or tired during the trial, which may also influence alpha power.
Although our design minimized the differences between valid and invalid conditions, the absolute effect of neurofeedback may be much smaller than previous studies For example, Ancoli and Kamiya (1978) suggested three critical factors to see positive effects of alpha feedback training, namely, (1) training for at least four sessions (2 h), (2) using continuous tone for feedback along with periodic scores of progress, and (3) using training trials with duration of at least 10 min. Thus, it is possible that more training sessions either on the same day or on different days could have led to long-term alpha enhancement, as observed in previous studies (van Boxtel et al., 2012;Dekker et al., 2014). Also, since we had a rather low ratio of valid to invalid trials (2:1), learning during training through operant conditioning may have been inefficient. In our design, the ratio was kept at 2:1 to have enough trials in each type (valid, invalid, and constant) to compare the effect of the neurofeedback training across type types. A lower proportion of invalid trials would have increased the duration of each experiment, which could have other disadvantages such as changes in the state of the subject due to drowsiness and fatigue, or changes in the impedance of the EEG electrodes. Further, as trials of different types were presented randomly, there might be a "carryover" effect of the training from one trial to the next. To reduce this effect, we provided sufficiently long inter-trial interval; participants were instructed to indicate when they wanted to start the next trial, such that a typical inter-trial interval was ϳ10 s or more. Even within each trial, participants were asked to keep their eyes open for the first 15 s, and the main effect of feedback was studied only after that. However, any carryover training effect that is longer than the inter-trial duration may have influenced the power in the next trial, mixing the effects of valid and invalid feedback.
However, while these factors explain why the effect of neurofeedback was smaller than many previous studies, they cannot explain our main result, which is a significant difference in alpha power between valid and invalid conditions in almost half of the participants (25% after Bonferroni correction). Indeed, the main point here is not that the effect of neurofeedback was weak, but that there was a significant effect of neurofeedback despite several design limitations that were incorporated to keep the valid and invalid conditions as similar as possible.
One way to overcome the distortion in the learning dynamics because of invalid trials could be to use an alternate strategy in which subjects are asked to upregulate or downregulate their alpha power in different blocks of trials, while providing valid feedback in both conditions. To our knowledge, such a design has not been used yet, although both upregulation and downregulation have been studied in different experiments (van Boxtel et al., 2012;Ros et al., 2013). However, such a design need not necessarily provide the same type of control as the invalid trials in our design. For example, participants may use different strategies to control the alpha power in the up versus down regulation conditions, which might again affect the learning dynamics for either type of task. In case there is a difference in alpha power in upregulation and downregulation conditions, it could be due to a subjects' ability to suppress alpha in downregulation condition instead of enhancement in the upregulation condition. So, if we are specifically interested in whether alpha can be voluntarily enhanced by valid feedback, an invalid feedback (unknown to the subject) may provide a more direct control. Further, this invalid feedback condition has been used in many earlier studies (albeit always on a different control group of participants), so our design follows a popular, well studied paradigm. This alternate strategy of interleaved blocks of upregulation and downregulation, nonetheless, can be used in future studies to provide a different type of control that can complement the control used in this study.

Neurofeedback and attention
Unlike previous studies where participants were asked to focus on the tone to control their alpha activity (Kamiya, 1969;Nowlis and Kamiya, 1970;Plotkin, 1978), in our study the participants were completely free to ignore the tone if the tone was distracting or did not aid in improving their performance score. We found that participants, who used the feedback tone for getting information about their alpha power without focusing too much to it, were the ones who could successfully maintain their alpha level. This is consistent with previous reports that have shown that attending to a stimulus leads to reduction in alpha power (Kelly et al., 2006b;Klimesch et al., 2007;Sadaghiani et al., 2010;Händel et al., 2011). Similarly, it is likely that attending to the neurofeedback tone may have reduced alpha power.
In our study, the main analysis was performed when the subjects had their eyes closed. This also may have contributed to the small effect of neurofeedback, since alpha power is much stronger when eyes are closed and may have reached some sort of "saturation level." Indeed, some previous studies have shown larger alpha enhancement when eyes were kept open (Brown, 1970;Zoefel et al., 2011;van Boxtel et al., 2012), even with no or invalid feedback (Ros et al., 2013;Enriquez-Geppert et al., 2014;Jurewicz et al., 2018). Even in our results, a weak but significant long-term enhancement in alpha power was indeed observed during the eye open condition. We preferred the eye closed state because this condition has fewer confounding variables, such as saccadic eye movements, which are known to modulate the power and phase in many frequency bands, including alpha (Bartlett et al., 2011;Staudigl et al., 2017). As before, while the eyes closed state may have resulted in a smaller overall effect of neurofeedback, this cannot explain the difference in alpha power between the valid and invalid conditions that we observed.
As opposed to the testing (neurofeedback) period, the baseline power used for calibration was recorded when the eyes were open (during the calibration period). This was done because we were particularly interested in quantifying the effect of neurofeedback in enhancing alpha activity from a baseline level where least amount of alpha activity was present. Furthermore, taking baseline measurement during eyes open state allowed the participants to feel a "definitive signal" when they closed their eyes since the tone frequency increased instantaneously. Comparison of alpha in eye open versus eye closed conditions is complicated, since different subjects might have different levels of alpha synchronization on eyes closure which may not be directly related to the eyes open state. In our case, this issue is of less relevance because our main comparison (between the valid and invalid conditions) is always during eye closed state only. Note that taking baseline measurement with eyes closed condition only changes Pc in Equation 1, which only shifts the operating frequency of the feedback tone away from 1000 Hz (Eqs. 1, 2) without changing any other dynamics.
Another potential confound could be related to the use of FCz as a reference electrode, since this electrode is near the C3 and C4 electrode positions where mu rhythms (which approximately have the same frequency range as alpha) might be predominant (Gastaut et al., 1954). However, mu rhythms are typically associated with planning of motor movements (Pfurtscheller and Neuper, 1997), but our participants were not engaged in any type of motor activity. Thus, it is unlikely that the choice of the reference electrode affected our results.

Mechanisms of alpha neurofeedback
Our results show a short-term benefit of valid neurofeedback in alpha power maintenance that does not translate to any long-term benefits. Neural mechanisms behind such short-term effects are unclear. Recent EEG-fMRI studies have demonstrated that neurofeedback can lead to a plastic increase in the connectivity within the salience network, which was detectable several minutes after the termination of training (Ros et al., 2013). Further, the increase in salience (default-mode) network connectivity was negatively (positively) correlated with changes in "on task" mind-wandering as well as resting state alpha rhythm (Ros et al., 2013). Default mode network, which primarily consists of the ventral medial prefrontal cortex (vmPFC) and posterior cingulate cortex (PCC), shows significant activity while individuals are not engaged in the external environment and are at a resting-state condition (Buckner et al., 2008;Uddin et al., 2009). On the other hand, salience network of the brain is active during the performance of sensory attention task (Sadaghiani et al., 2010). Neurofeedback can also change dynamic resonant loops in the cortical and thalamocortical circuit (Lubar, 1997), potentially by changing their excitability (Ros et al., 2010). Unfortunately, because we only recorded from occipital electrodes, we cannot study the interaction between visual and default mode or salience networks or measure changes in the excitability of different brain structures. Even if we had coverage of the entire brain, significant volume conduction and poor source localization with EEG (Nunez et al., 1997;Nunez and Srinivasan, 2006) would likely have made analysis and interpretation of data difficult. Simultaneous fMRI-EEG recording while providing neurofeedback, similar to the study by Ros et al. (2013), may be needed to better understand the effect of neurofeedback at short time scales.
Behaviorally, neurofeedback training was perceived relaxing by almost all the participants, with an average subjective relaxation score of 7.96 Ϯ 0.21 out of 10, consistent with previous studies (Kamiya, 1969;Brown, 1970;Nowlis and Kamiya, 1970), although there was no increase in alpha power over trials and the change in alpha power between valid and invalid trials was uncorrelated with the relaxation score (Fig. 4B). Instead, this relaxation may be attributed to various factors described by Plotkin, which include sensory deprivation, sustained alertness, concentration/meditation, introspective sensitization, expectation, perceived success at the feedback task due to the isolated setting during the neurofeedback training (Plotkin, 1978(Plotkin, , 1979. Thus, while we show that neurofeedback indeed leads to an increase in alpha power even under the most stringent control conditions and show that this works best for subjects who otherwise cannot sustain their alpha power and when they attend to the feedback "passively" (that is, have intermediate attention scores), we do not comment on its potential beneficial physiological effects. Since such different types of feedback are inter-mixed in our design, such questions are beyond the scope of our study.