Audio–Visual Fission Illusion and Individual Alpha Frequency: Perspective on Buergers and Noppeney (2022)

Abstract Integrating visual and auditory information is an important ability in various cognitive processes, although its neural mechanisms remain unclear. Several studies indicated a close relationship between one's temporal binding window (TBW) for audio–visual interaction and their alpha rhythm in the brain (individual alpha frequency or IAF). A recent study by Buergers and Noppeney [Buergers, S., & Noppeney, U. The role of alpha oscillations in temporal binding within and across the senses. Nature Human Behaviour, 6, 732–742, 2022], however, challenged this view using a new approach to analyze behavioral data. Conforming to the same procedures by Buergers and Noppeney, here, I analyzed the data of my previous study and examined a relationship between TBW and IAF. In contrast to Buergers and Noppeney, a significant correlation was found between occipital IAF and a new behavioral measure of TBW. Some possibilities that caused these opposing results, such as a variability of “alpha band” across studies and a large inter-individual difference in magnitude of the fission illusion, are discussed.


INTRODUCTION
Multisensory integration is a key function to perceive our environment efficiently (Hirst, McGovern, Setti, Shams, & Newell, 2020;Keil, 2020;Zhou, Cheung, & Chan, 2020).Of particular importance in everyday life is an integration between visual and auditory inputs, which plays a crucial role in speech perception (Conrey & Pisoni, 2006), person recognition (Robertson & Schweinberger, 2010) and emotional processing (Walker-Andrews, 1997), and so forth.It is known that temporal synchrony provides a critical cue for this audio-visual integration (Dixon & Spitz, 1980;Vroomen & Keetels, 2010).To be combined into a coherent percept, visual and auditory stimuli must co-occur within a limited interval that is called the temporal binding window (TBW).
Many studies have explored neural underpinnings of the TBW.In the research of visual perception, alpha oscillations (8-13 Hz) have been proposed to play a critical role in parsing visual inputs into discrete events ( VanRullen, 2016).For example, two flashes successively presented were perceived as a single event when they fell into one alpha cycle, whereas those falling into separate cycles were perceived as two different events (Samaha & Postle, 2015).These results support a view that alpha rhythm serves as TBW through which a constant influx of visual signals is segmented into temporal units.Recent studies further provided a direct link between the speed of alpha rhythms and performance efficiency in visual and visuospatial cognitive tasks (Bertaccini et al., 2022;Di Gregorio et al., 2022).
The close relationship between alpha cycle and TBW has been also reported in audio-visual interaction.Using the sound-induced double-flash (fission) illusion (Shams, Kamitani, & Shimojo, 2000), a typical example of an audiovisual integration, Cecere, Rees, and Romei (2015) reported that lower frequency of individual alpha rhythm (individual alpha frequency or IAF) was associated with a higher occurrence rate of the fission illusion (Cecere et al., 2015).Several studies have replicated this finding (Noguchi, 2022;Cooke, Poch, Gillmeister, Costantini, & Romei, 2019;Keil & Senkowski, 2017).These results indicate a link between one's duration of alpha cycle with audio-visual TBW; lower alpha rhythm provided a broader temporal unit for an audio-visual interaction, resulting in higher rate of an illusory flash induced by concurrent beeps.However, Buergers and Noppeney (2022) recently provided the data inconsistent with this view; they found no evidence for a relationship between IAFs and TBWs (Buergers & Noppeney, 2022).Neural correlates of the audio-visual TBW, therefore, is a matter of intense debate.
A hallmark of Buergers and Noppeney (2022) was that they separately investigated the effects of alpha frequency on two behavioral measures of the signal detection theory; sensitivity (d 0 ) and bias (Bias center ).Perceptual sensitivity is an index for a temporal resolution (precision) of a sensory system, whereas bias reflects a tendency of reporting one particular percept (e.g., "two flash" response in the fission illusion).Buergers and Noppeney (2022) reported that neither the sensitivity nor bias for two-flash discrimination was associated with peak IAFs of 20 observers.
Inspired by their approach, here I re-analyzed the data in Noguchi (2022) and correlated the d 0 and bias for the fission illusion with IAF.Below are brief descriptions about stimuli, task, and data analyses (see Noguchi [2022] for details).

METHODS
Twenty-nine healthy participants (18-42 years) took part in the study.Data of two participants were discarded because of an excessive noise in EEG waveforms and thus replaced by those of two additional participants.This sample size (29) was determined by a power analysis (Type I error rate: 0.05, statistical power: 0.80, effect size: r = .5).An informed consent was obtained from each participant, and all experiments were carried out along with the guidelines and regulations of the ethics committee at Kobe University, Japan.
Structures of one trial was shown in Figure 1A.A combination of zero to two flashes (white circle, diameter: 4.69°, luminance: 55 cd/m 2 ) with zero to two beep sounds (pure tone, frequency: 4000 Hz, duration: 8 msec) produced eight types of trials; 0F1S (no-flash with one sound), 0F2S, 1F0S, 1F1S, 1F2S, 2F0S, 2F1S, and 2F2S.The flash was presented on a CRT monitor with the duration set at one frame of a refresh rate (60 Hz or 16.7 msec), although actual duration might be shorter because of phosphor decay rate (Ferri, Venskus, Fotia, Cooke, & Romei, 2018;Elze, 2010).A SOA between two flashes and that between two sounds were both set at 50 msec (Figure 1B).Participants reported the perceived number of flashes (zero, one, or two), ignoring all sounds.The eight types of trials were randomly intermixed in an experimental session of 126 trials.The flash was presented in a left visual field (eccentricity: 12.5°) for three experimental sessions but in a right field for the other three.
Behavioral data were analyzed conforming to procedures in Buergers and Noppeney (2022).First, I computed a perceptual sensitivity (d 0 ) and a response bias (Bias center ) when participants discriminated one-flash from two-flash trials under no sound (shown in green in Figure 1C).Using the data of 1F0S and 2F0S trials, they were obtained through the equations below: where the hit rate (HR) was a proportion of "two flash" responses in 2F0S trials and the false-alarm rate (FAR) was a proportion of "two flash" responses in 1F0S trials.
Likewise, another set of d 0 and Bias center to discriminate one flash versus two flashes under one sound was computed using the HR in 2F1S trials and FAR in 1F1S trials (blue in in Figure 1C).A final set of d 0 and Bias center in the two-sound context was obtained from the HR in 2F2S and FAR in 1F2S trials (red in in Figure 1C).The audio-visual fission illusion would be observed as a reduced d 0 in the two-sound context.Furthermore, if the fission illusion also involved a change in bias, this would be seen as a reduced Bias center in the two-sound context, because Bias center < 0 indicates that participants were more likely to report a two-flash than one-flash percept regardless of their perceptual sensitivities.EEG signals were measured from 32 points over the scalp (Biosemi ActiveTwo system, sampling rate: 2048 Hz, analog low-pass filter: 417 Hz).Sensors of interest were set at O1, O2, and Oz (shown in red in Figure 1D) in light of a previous literature on alpha frequency and the fission illusion (Buergers & Noppeney, 2022;Cooke et al., 2019;Keil & Senkowski, 2017;Cecere et al., 2015).Using the Brainstorm toolbox for MATLAB (Tadel, Baillet, Mosher, Pantazis, & Leahy, 2011), EEG data of each trial (from −1000 to 0 msec relative to the first flash or sound) were converted into power spectral density (PSD).I confirmed by visual inspection that EEG waveforms in this period did not contain large noise after an application of digital band-pass filter (0.5-200 Hz, Butterworth).The conversion to PSD was performed by the Welch's method (Hamming window, length: 1000 msec).No zero-padding technique was used.A peak frequency in alpha band (8-13 Hz) was then identified by searching a component frequency with a maximum power on the PSD.A trait alpha frequency for each participant was computed as an average of the peak frequencies across all 756 trials.For comparisons, peak frequencies of other bands (delta: 1-4 Hz, theta: 4-8 Hz, beta: 13-30 Hz, gamma: 31-58 Hz, and high gamma: 62-100 Hz) were also identified and correlated with d 0 (Figure 2A) and Bias center (Figure 2B).
In addition to the main analysis described above, I performed two analyses to test the robustness of the present data.First, IAF was computed using the data only in the two-sound trials (2F2S and 1F2S), not all 756 trials.This would match the data set for computing behavioral measure (d 0 or Bias center ) with that for EEG measure (IAF), enabling a fair comparison of those two (Figure 3A).Second, a time window of EEG analysis was set at −400 to 0 msec (Figure 3B), not −1000 to 0 msec.As shown in Figure 1A, a prestimulus period consisted of a blank screen of 500 msec followed by a fixation screen of 500-600 msec.Setting a time window at −400 to 0 msec might provide a better EEG measure that was not contaminated by visual response to an onset of the fixation point.A use of shorter time window, however, reduces frequency resolution of PSD.I resolved this issue by pooling EEG waveforms of all trials into a single (long) waveform.The Welch's method was applied to this long (concatenated) waveform to get a PSD for each participant.

RESULTS
Perceptual sensitivity to discriminate one flash versus two flashes (d 0 ) is displayed in the left in Figure 1C.A one-way ANOVA over the three auditory contexts (zero sound/one sound/two sounds) yielded a significant main effect, F(2, 56) = 13.94,p < .001,η 2 = .33.Post hoc tests with the Bonferroni correction indicated significant differences between zero sound versus one sound ( p < .001)and between zero sound versus two sounds ( p < .001).The one-way ANOVA with the Greenhouse-Geisser adjustment also yielded a significant main effect for the Bias center (right panel of Figure 1C, F(1.54, 43.21) = 145.56,p < .001,η 2 = .84)with post hoc differences of all three pairs significant ( p < .001).These data replicated Buergers and Noppeney (2022) at least for the fission illusion (two sounds).
Figure 2A shows r-maps between behavioral and EEG data.A correlation coefficient between the d 0 (two sounds) and peak frequency was calculated for each sensor position and color-coded over a 2-D layout of the 32 sensors (Figure 1D).Positive correlations with d 0 (shown in red) were selectively observed in peak alpha frequency (upper right).Correlations at occipital sensors (Oz: r = .49,O1: r = .38,and O2: r = .40)were all significant ( p < .05,shown by black dots), indicating that individuals with higher alpha frequency showed larger d 0 (less fission illusion).In contrast, the alpha frequencies over the occipital cortex showed no significant correlation with Bias center (Figure 2B, Oz: r = .34,O1: r = .32,and O2: r = .34),although strong correlations were seen over the nonoccipital (temporal and frontal) regions (e.g., CP5: r = .49).
Results of the two additional analyses (see Methods section) are shown in Figure 3.I displayed in Figure 3A the r-maps in which IAF was computed from the data of the two-sound trials (2F2S and 1F2S).Similar to Figure 2, significant correlations with d 0 , but not Bias center , were observed at occipital sensors.Figure 3B shows the r-maps in which IAF was identified with a prestimulus data of −400 to 0 msec.The r-maps in the top indicate correlations between peak alpha frequency (pooled across all 756 trials) and behavioral measures, whereas those in middle indicate the correlation between central alpha frequency and behavioral measures.The central frequency was defined as a mean of component frequencies at alpha range (8-13 Hz) weighted by their powers.The r-maps of the central frequency on the two-sound trials are shown in the bottom of Figure 3B.The significant correlations between IAF with d 0 over the occipital cortex were consistently seen (Oz: r = .41∼ 0.50) in all analyses.

DISCUSSION
In contrast to Buergers and Noppeney (2022), the present data support a close relationship between occipital IAF and one's temporal resolution of audio-visual integration (d 0 ).How can we resolve this inconsistency?I provide below three possibilities that might reconcile the opposing results.
First, whereas Buergers and Noppeney (2022) searched for an IAF within a band of 6-14 Hz, I identified it using a narrower band of 8-13 Hz. Figure 2A suggest that a correlation between d 0 and peak frequency is highly selective to alpha band; no positive correlation with d 0 was observed in the r-map of individual theta (4-8 Hz) or beta (13-30 Hz) frequency.Although a definition of alpha band has been variable across studies, a use of a narrower band might be suitable to detect a relationship of IAF with the audiovisual TBW.Indeed, I observed a reduction in correlation coefficient at Oz (from .42 to .15) when an IAF was searched within the broader band of 6-14 Hz (Figure 3C,left).
Second, a detection of significant correlation might be prevented by the bias or a large intersubject variability in magnitudes of the fission illusion.As Buergers and Noppeney (2022) recognized, their data of individual TBWs measured by a classical method (psychometric thresholds) were susceptible to the bias and an intersubject variability.As a result, a scatterplot in their Yes-No SOA task (Figure 4b in Buergers & Noppeney, 2022) contained at least 6 outliers (out of 19) whose psychometric thresholds were unmeasurable.Excluding these outliers might reveal a negative correlation between IAFs and behavioral TBWs.Indeed, Keil and Senkowski (2017) showed a relationship between IAFs and rates of the fission illusion by excluding the data of 14 participants (out of 40) whose illusion rates were too high (> 90%) or too low (< 10%).The present data also suggest an effectiveness of the data screening.In the right of Figure 3C, I discarded the data of 10 participants who showed low task accuracy or no fission/fusion illusion (see Noguchi [2022], for precise criteria).The r-map of the remaining  Buergers and Noppeney (2022), this caused a decrease in correlation coefficient (left).In contrast, correlations over the occipital cortex were kept significant when the data of participants who showed low task accuracy or no fission/fusion illusion were excluded from the analysis (right).
19 participants indicated a positive correlation between d 0 and central IAF over a wide region in the occipital cortex (Oz: r = .51).
Finally, it is preferable to correlate behavioral and EEG data simultaneously recorded.In Buergers and Noppeney (2022), their two-interval forced-choice task provided an excellent behavioral measure that can reduce an effect of the bias.This measure, however, was correlated with EEG data in a resting (eyes-closed) session or different task sessions.Keil and Senkowski (2017) reported that, although the illusion rates were significantly correlated with IAFs simultaneously obtained, no correlation was seen when those rates were compared with resting-state IAFs.A combination of bias-free behavioral measure with simultaneous EEG data would benefit future studies to examine a relationship between the fission illusion and IAF.
On the other hand, there are some points to be improved in the present data.A major problem would be that I fixed the SOA between two flashes/sounds at 50 msec.Whereas Buergers and Noppeney (2022) tested a variety of SOAs ranging from 25 to 225 msec, only one SOA (50 msec) was implemented in the present study.Such an approach can seriously suffer from the problem of inter-individual variability described above.Setting appropriate SOAs that can cover the individual differences, hopefully through a preliminary thresholding procedure, would resolve this issue and provide better behavioral measures for the fission illusion.

Figure 1 .
Figure 1.Experimental procedures and behavioral results.(A) Structures of one trial, reprinted from Noguchi (2022) with permission.Participants reported the number of flashes, neglecting all sounds.(B) Sequences of visual and auditory stimuli in the one-flash and two-sounds (1F2S) trial (left) and the 2F2S trial (right).(C) Behavioral results.In each of three contexts (zero sound/one sound/two sounds), perceptual sensitivity (d 0 ) and response bias (Bias center ) were computed and shown in left and right panels, respectively.Larger d 0 indicate a higher temporal resolution of visual system to discriminate one flash versus two flashes.Larger Bias center indicates that participants were more likely to report a one-flash than two-flash percept.(D) Twodimensional layout of 32 EEG sensors.***p < .001.

Figure 2 .
Figure 2. Correlation of behavioral and EEG measures.(A) r-maps between individual peak frequency and d 0 in the two-sound context (fission illusion).EEG sensors with significantly positive correlations ( p < .05)are shown by black dots, whereas those with negative correlation are shown by white dots.(B) r-maps between individual peak frequency and Bias center in the two-sound context.Peak alpha frequencies at occipital sensors were significantly correlated with d 0 (A) but not with Bias center (B).

Figure 3 .
Figure 3.The r-maps of additional analyses.(A) Correlations between IAF and behavioral measures (d 0 and Bias center ).Although IAFs in Figure 2 were computed using the data of all (756) trials, those in this panel were obtained from 216 trials in the two-sound context (2F2S and 1F2S).(B) r-maps between behavioral measures and IAF at −400 to 0 msec (not at −1000 to 0 msec).Data of individual peak frequency, central frequency, and the central frequency of the two-sound trials are shown in top, middle, and bottom panels, respectively.(C) An effect of bandwidth and a screening of participants.When the central frequency was computed with a broader alpha band of 6-14 Hz, as inBuergers and Noppeney (2022), this caused a decrease in correlation coefficient (left).In contrast, correlations over the occipital cortex were kept significant when the data of participants who showed low task accuracy or no fission/fusion illusion were excluded from the analysis (right).