Phase shifts in alpha-frequency rhythm detected in electroencephalograms influence reaction time

Accepted Manuscript Phase shifts in alpha-frequency rhythm detected in electroencephalograms influence reaction time Yasushi Naruse, Ken Takiyama, Masato Okada, Hiroaki Umehara, Yutaka Sakaguchi PII: DOI: Reference:

S0893-6080(14)00178-6 http://dx.doi.org/10.1016/j.neunet.2014.07.012 NN 3373

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Neural Networks

Please cite this article as: Naruse, Y., Takiyama, K., Okada, M., Umehara, H., & Sakaguchi, Y. Phase shifts in alpha-frequency rhythm detected in electroencephalograms influence reaction time. Neural Networks (2014), http://dx.doi.org/10.1016/j.neunet.2014.07.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Phase shifts in alpha-frequency rhythm detected in electroencephalograms influence reaction time Yasushi Narusea,∗, Ken Takiyamab,c , Masato Okadad,e , Hiroaki Umeharaa , Yutaka Sakaguchif Center for Information and Neural Networks (CiNet), National Institute of Information and Communications Technology and Osaka University, Kobe, Hyogo 651-2492, Japan b Japan Society for the Promotion of Science, Kojimachi, Tokyo 102-0083, Japan c Brain Science Institute, Tamagawa University, Machida, Tokyo 194-8610, Japan d Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8561, Japan e RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan f Graduate School of Information Systems, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan

a

Abstract Although the phase shifts in ongoing oscillations seen in electroencephalograms (EEGs) and magnetoencephalograms are an important factor in discussions of phase dynamics, such as synchrony and reset, few studies have focused specifically on the phase shift. Here we investigate the relationship between phase shifts in alpha-frequency rhythms and reaction times during a visual simple reaction task by applying our previously described method [Naruse, Y., Takiyama, K., Okada, M., and Umehara, H. (2013). Statistical method for detecting phase shifts in alpha rhythm from human electroencephalogram data. Phys Rev E, 87, 042708], which enables detection of ∗ Corresponding address: National Institute of Information and Communications Technology, 588-2 Iwaoka, Iwaoka-cho, Nishi-ku, Kobe 651-2492, Japan. Tel: +81-78-969-2225; fax: +81-78-969-2279. Email address: [email protected] (Yasushi Naruse)

Preprint submitted to Neural Networks

July 30, 2014

phase shifts from a single EEG trial. In the left, parietal, and occipital areas, the reaction times in the trials in which phase shifts were detected before the button press were significantly longer than in those in which phase shifts were not so detected. These results indicate that phase shifts in the alpha and mu rhythms relate to variability in reaction times. Keywords: Phase shift, Reaction time, EEG, Alpha rhythm, Mu rhythm, State-space model, Bayes’ theorem 1. Introduction The ongoing oscillations, i.e., alpha, beta, gamma, theta, and mu rhythms, seen in electroencephalograms (EEGs) and magnetoencephalograms (MEGs) exhibit a feature that has recently been gaining attention: they are synchronized (Rodriguez et al., 1999; Lachaux, Rodriguez, Martinerie & Varela, 1999; Varela, Lachaux, Rodriguez & Martinerie, 2001; Mizuhara & Yamaguchi, 2007) and reset (Makeig et al., 2002; Naruse, Matani, Hayakawa & Fujimaki, 2006; Palva & Palva, 2007) by external stimuli. Although these oscillations include both amplitude and phase components, here we focus on the latter because phase is the more important factor in discussing synchrony and reset. In phase synchronization, the phases are shifted by external stimuli so that they are synchronized across more than two brain regions. In phase reset, the phases are rapidly changed by external stimuli. Thus, the ability to detect phase shifts is essential to understanding these phenomena. To detect these shifts—in particular, phase resets—some previous studies have averaged data from many trials because of the low signal-to-noise ratio of EEG and MEG signals (Makeig et al., 2002; Naruse et al., 2006). 2

The averaging method can detect only the phase-locking type of shifts that occur with similar timings over many trials. Other studies have detected phase shifts from single-trial data by using the Hilbert transform (Freeman, Burke & Holmes, 2003; Kozma, Davis & Freeman, 2012). However, phase shifts detected with this method have tended to concentrate in low-amplitude intervals (Freeman et al., 2003), raising the suspicion that they may be artifacts, perhaps caused by a loss of precision in the low-amplitude data. In an earlier study, we reported a novel statistical method that can detect phase shifts in the alpha rhythm from a single EEG trial (Naruse, Takiyama, Okada & Umehara, 2013). This method uses state-space models (SSMs) and the line-process (LP) technique (Geman & Geman, 1984). The LP technique is a Bayesian method that can detect discontinuous changes in time series data. One important feature of our method is that it detects phase shifts most effectively when the amplitude is high and, accordingly, avoids false detections owing to imprecision in low-amplitude data (Naruse et al., 2013). However, the feature tends to increase the miss of the detection of the phase shift in low-amplitude data. The results from flash-response EEG data showed that there are non-phase-locking shifts that occur at differing times among trials, which cannot be detected by the averaging method. Our previous work mentioned only the dynamics of the phase shifts in the alpha rhythm; the functional role of these shifts in the alpha rhythm remains unclear. Several studies have revealed the relationship between the phase of the alpha rhythm at stimulus onset and brain function, such as visual awareness (Mathewson, Gratton, Fabiani, Beck & Ro, 2009), perceptual framing (Varela, Toro, John & Schwartz, 1981), and reaction times (RTs) (Callaway

3

& Yeager, 1960). In this study, we focus on the influence of the phase of the alpha rhythm on RTs because this problem has been outstanding since 1960. Callaway and Yeager first reported that the phase of the alpha rhythm at stimulus onset significantly influences RTs during a visual simple reaction task, and they concluded with the observation that “finer details of the relationship between alpha phase and reaction time must wait further investigation” (Callaway & Yeager, 1960). Decades afterward, the finer details are still unclear. To our knowledge, there is no study that discusses the relationship between phase shifts in the alpha rhythm and RTs. By focusing on the influence of phase shifts on RTs, we expect that the functional role of these shifts can be elucidated. For instance, Freeman et al. have hypothesized that phase shifts represent state transitions in the brain (Freeman et al., 2003). If this is the case, then the RTs in a trial in which a phase shift is detected before a button press could differ from those in a trial that detects no such shift. While the alpha rhythm occurs over the posterior regions of the brain, there is another rhythm at the alpha frequency (8–13 Hz) that occurs over the central or centro-parietal region, the mu rhythm, which relates to motor control (Chatrian, Bergamini, Dondey, Klass, Lennox-Buchthal & Petersen, 1974). Phase shifts in the mu rhythm also may be connected to RTs. In this study, we investigate the relationship between phase shifts in the rhythms of alpha frequency and RTs during a visual simple reaction task.

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2. Method 2.1. Phase-shift detection in a single trial Our method for detecting phase shifts in a single trial was proposed in Naruse et al. (2013), to which we refer the reader for more detail. The EEG data at the sampling point k is denoted by yk . We assume that yk includes the alpha-frequency rhythm and independent observation noise between sampling points. Thus, it is expressed as yk = ak cos xk + ξ, where xk and ak denote the instantaneous phase and amplitude of the rhythm of the alpha frequency at sampling point k, respectively, and ξ denotes the observation noise. Note that the domain of the phase is [0, 2π) and that of the amplitude is [0, ∞). Here we assume the noise is Gaussian, and hence the likelihood function is p(yk | ak , xk , α) =

r

  α α 2 exp − (yk − ak cos xk ) , 2π 2

(1)

where α is a hyperparameter that controls the strength of the observation noise. We define the prior distribution of the phase using the von Mises distribution and the SSM as P −1 p p exp{ N p n=1 [(1 − ln )β cos(xn+1 − xn − ω) − ln κ]} p(x, l | β, ω, κ) = , Zp (β, κ)

(2)

where x = {x1 , x2 , . . . , xN }, lp = {l1p , l2p , . . . , lNp −1 } ∈ {0, 1}N −1 , and Zp (β, κ) indicate the instantaneous phase, the parameter for the phase shift based on the LP technique, and the normalization constant of p(x, lp | β, ω, κ), respectively. The hyperparameters β, ω, and κ control the amount of phase fluctuation, the individual alpha frequency, and the frequency of the phase shift, respectively. N is the number of sampling points; lkp = 1 indicates the 5

occurrence of a phase shift in the time bin between the kth and (k + 1)st sampling points, and lkp = 0 indicates a smooth phase change. Similarly, we define the prior distribution of the amplitude using the Gaussian distribution and the SSM as PN −1 a a 1 2 exp({ n=1 {(1 − ln )[− 2 γ(an+1 − an ) ] − ln λ}) a , p(a, l | γ, λ) = Za (γ, λ)

(3)

where a = {a1 , a2 , . . . , aN }, la = {l1a , l2a , . . . , lNa −1 } ∈ {0, 1}N −1 , and Za (γ, λ) indicate the instantaneous amplitude, the parameter for the amplitude shift based on the LP technique, and the normalization constant of p(a, la | γ, λ), respectively; the hyperparameters γ and λ control the magnitude of the amplitude fluctuation and the frequency of the amplitude shift, respectively. Similarly to the case of the phase shift, lka = 1 indicates the occurrence of an amplitude shift and lka = 0 indicates a smooth amplitude change at the time bin between the kth and (k + 1)st sampling points. Assuming that the prior distributions of the phase and amplitude are independent, we can express the posterior distribution based on Bayes’ theorem as p(y | a, x, α)p(x, lp | β, ω, κ)p(a, la | γ, λ) , p(a, x, l , l | y, α, β, γ, ω, κ, λ) = Z(α, β, γ, ω, κ, λ) (4) p

a

where Z(α, β, γ, ω, κ, λ), which is equal to p(y | α, β, γ, ω, κ, λ), is the normalization constant of p(a, x, lp , la | y, α, β, γ, ω, κ, λ).

We estimated the hyperparameters on the basis of type II maximum likelihood estimation. Their estimated values are   H Y ˆ γˆ , ω ˆ = arg Zh (α, β, γ, ω, κ, λ) , {ˆ α, β, ˆ, κ ˆ , λ} max {α, β,γ, ω, κ, λ}

6

h=1

(5)

where H indicates the number of trials. When marginalizing the posterior distribution between sampling points k and k + 1, we can calculate the probabilities of four states: S1) Both the phase and amplitude are smooth [p(lkp = 0, lka = 0) = p(lkp = 0)× p(lka = 0)] ; S2) Only the phase is shifted [p(lkp = 1, lka = 0) = p(lkp = 1)p(lka = 0)] ; S3) Only the amplitude is shifted [p(lkp = 0, lka = 1) = p(lkp = 0)p(lka = 1)] ; and S4) Both are shifted [p(lkp = 1, lka = 1) = p(lkp = 1)p(lka = 1)]. By comparing the probabilities of these four states, we can estimate the state at each time bin. In this study, we focus on the phase shift, and therefore, we define a phase shift to have been detected in the bin between sampling points k and k + 1 if S2 or S4 has the highest probability among the four states. 2.2. EEG experiments We used the data described in Naruse, Takiyama, Okada & Murata (2010). EEG data from six clinically normal adult volunteers with their eyes closed were recorded. None of the subjects had any history of relevant neurological or visual disorders. All subjects gave written informed consent. The study received ethical approval from the Ethics Committee for Human and Animal Research at the Graduate School of Frontier Sciences, University of Tokyo. Flash stimuli were projected onto a screen (visual angle 50◦ × 60◦ ,

luminance 730 cd/m2 ). Their duration was 1/60 s, and the interstimulus interval was randomly selected to be between 2 and 4 s. The EEG data were 7

recorded in five experimental blocks, each consisting of 100 trials. Subjects were provided adequate rest between blocks. The subjects were asked to press a button with their right index finger as soon as they perceived a flash. To remove the effects of outliers, we excluded trials in which the RTs were shorter than 150 ms or longer than 500 ms. The EEGs were recorded using a cap with 30 Ag-AgCl electrodes and referenced to the right earlobe. The input impedances of all electrodes were below 10 kΩ. The data were sampled at 1 kHz, digitally bandpass filtered between 5 and 45 Hz, and downsampled to 100 Hz. We defined four areas for the following analysis (Fig. 1). The left area (LA) includes electrodes FC3, C3, and CP3. The right area (RA) includes FC4, C4, and CP4. The parietal area (PA) includes P3, Pz, and P4. The occipital area (OA) includes O1, Oz, and O2. We defined a phase shift to have been detected in an area if a shift was detected from at least one channel in the area. 3. Results We applied our method to the EEG data for each area. First, we verified whether phase shifts caused by brain activity relating to the visual simple reaction task were detected by the method. We counted the number of detected phase shifts in each time bin for all trials, separately for each subject. Figure 2A shows the LA data, grand-averaged over all the subjects, as a typical result. Background phase shifts were detected in the prestimulus period, and the number of detected shifts increased during the poststimulus period. The time courses in the other areas were similar to that in LA. 8

FP1

F7

F3

FP2

FZ

LA

F4

F8

RA

FT7

FC3

FCz

FC4

FT8

T7

C3

Cz

C4

T8

TP7

CP3

CPz

CP4

TP8

P4

P8

PA P7

P3

Pz OA

O1

Oz

O2

Figure 1: Areas for the analysis. The left area (LA) includes electrodes FC3, C3, and CP3. The right area (RA) includes FC4, C4, and CP4. The parietal area (PA) includes P3, Pz, and P4. The occipital area (OA) includes O1, Oz, and O2.

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In all areas, the averaged values in the poststimulus period (0 to 0.5 s) were significantly larger than those in the prestimulus period (−0.5 to 0 s) (p < 0.00001; Wilcoxon rank-sum test with Bonferroni correction). This result indicates that our method successfully detected phase shifts caused by brain activity relating to the visual simple reaction task in the poststimulus period. Next we investigated the relationship between phase shifts and RTs. Table 1 shows the mean and standard deviation of the RTs for each subject. To normalize the difference in RTs between subjects, the RTs were z-scored within each subject. The z-scored RT, z, is defined as z = (r − u)/s, where r, u, and s denote the RT, the mean of the RTs, and their standard deviation, respectively. The z-scored RT takes negative and positive values for RTs below and above the mean, respectively. We defined a trial that detected a phase shift (hereafter ‘detected trial’) as one in which a phase shift was detected in the 150 ms before the button press in each area (Fig. 2B), since the shortest RT in the analyzed trials was 150 ms. Table 2 shows the number of detected and undetected trials in each area. The values were summed over all subjects. Fig. 3 shows the averages of z-scored RTs from detected and undetected trials of all subjects for each area. The RTs in the detected trials were significantly longer than those in the undetected trials in LA, PA, and OA (p < 0.05; Wilcoxon rank-sum test with Bonferroni correction). These results indicate that the RT tended to be longer when the phase shift in the rhythm of the alpha frequency occurred before the button press. 10

Table 1: Mean and standard deviation (SD) of RTs for each subject

Subject No.

Mean (ms) SD (ms)

1

254

32

2

209

55

3

267

71

4

358

112

5

262

61

6

224

56

We examined the distribution of the times at which phase shifts were detected in the 150 ms before a button press. Figure 4 shows histograms of these timings for LA, PA, and OA with respect to the presses. No clear tendency can be seen. 4. Discussion In the present study, we applied our method (Naruse et al., 2013) to EEG data during a visual simple reaction task. The number of trials in which phase shifts were detected in the poststimulus period was significantly larger than that in the prestimulus period (Fig. 2A), which suggests that our method successfully detected phase shifts caused by brain activity related to the task. Next, we investigated the relationship between the phase shift in the alpha-frequency rhythms and RTs. In LA, PA, and OA, the RTs in the detected trials were significantly longer than those in the undetected trials (Fig. 3). These results indicate that the phase shifts in rhythms of 11

Table 2: Number of detected and undetected trials for each area

Area

No. of detected trials

No. of undetected trials

LA

995

1879

RA

919

1955

PA

1086

1788

OA

632

2242

Note: Values were summed over all subjects.

alpha frequency relate to the variability of the RT among the trials. To our knowledge, this is the first study to directly show a relationship between brain function and phase shifts in the rhythm of alpha frequency. In the alpha-rhythm frequency range, the alpha rhythm occurs over the posterior visual region and the mu rhythm occurs over the central motor region (Chatrian et al., 1974). Therefore, LA and RA contain the mu rhythm as a major component of the alpha frequency, and OA contains the alpha rhythm as the major component. The result that phase shifts in OA are related to the RTs suggests that phase shifts in the alpha rhythm in the visual area affect the RTs, and the result that phase shifts in LA are related to the RTs and those in RA are not suggests that phase shifts in the mu rhythm in the contralateral motor area also affect the RTs. The greatest RT difference between the detected and undetected trials was seen in OA. We can calculate the approximate RT difference based on DS, where D and S denote the difference found in the average z-scored RTs between the detected and undetected trials and the mean of the RT standard

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deviations among the subjects, respectively. The RT difference in OA was approximately 8 ms, as the difference in average z-scored RT was 0.13 and the intersubject mean of the standard deviations was 64.5 ms. Our sampling interval was 10 ms (i.e., a sampling rate of 100 Hz), which is longer than the RT difference. Thus, the process corresponding to the phase shifts was presumably completed within a sampling interval, and it therefore seems reasonable that no clear tendency was seen in the phase-shift timings (Fig. 4). We have assumed that the noise obeys Gaussian distribution [Eq. (1)] for the sake of simplicity, since our method was able to detect EEG phase shifts for flash stimuli under the same assumption (Naruse et al., 2013). However, the noise might be non-Gaussian, since there are ongoing oscillations other than the alpha-frequency rhythm, and hence there exists the possibility that this assumption could degrade the detection performance. Nevertheless, the proposed method can be used in the same fashion even if the noise follows another distribution, simply by changing the Gaussian distribution in Eq. (1) to the appropriate form. Investigation of which distribution should be assumed for optimal performance is an important topic for future research. This study successfully showed that phase shifts in the rhythms of the alpha frequency relate to brain function. How do these influence the RT? This study unfortunately does not provide enough information to answer this question. One hypothesis that could explain our results is that the phase shifts represent state transitions in the brain (Freeman et al., 2003). A transition may occur if a stimulus is delivered when the brain is in a state in which a transition is required for stimulus processing. In this case,

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the brain has to wait until a phase shift is achieved, and as a result, the RT may be increased. Accordingly, the RTs from the trials in which phase shifts were detected before the button press are longer than those from trials in which phase shifts were not detected. To verify this hypothesis, further study is required to identify what constitutes a brain state that needs a state transition in the brain. Phase shifts are known to relate to phase synchronization (Kuramoto, 1984; Winfree, 1987), and phase synchronization of ongoing oscillations among brain areas is known to play an important role in brain functions (Rodriguez et al., 1999; Lachaux et al., 1999; Varela et al., 2001; Mizuhara & Yamaguchi, 2007). Therefore, brain state may depend on the state of synchronization among different areas. Thus, a detailed investigation of the relationship between phase shifts and phase synchronization among brain areas is needed. However, the spatial resolution of EEGs is low, and therefore they are not suitable to verifying this hypothesis. Since the spatial resolution of MEGs is higher than that of EEGs (Hamalainen, Hari, Ilmoniemi, Knuutila & Lounasmaa, 1993), in the future we will investigate the relationship between synchronization among brain areas and phase shifts by using MEG. Acknowledgments This work was partially supported by Grants-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (KAKENHI No. 21120012) and the Japan Society for the Promotion of Science (KAKENHI No. 24700422).

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References Callaway, E., & Yeager, C. L. (1960). Relationship between reaction time and electroencephalographic alpha phase. Science, 132 , 1765–1766. Chatrian, G. E., Bergamini, L., Dondey, M., Klass, D. W., Lennox-Buchthal, M., & Petersen, I. (1974). A glossary of terms most commonly used by clinical electroencephalographers. Electroen Clin Neuro, 37 , 538–548. Freeman, W. J., Burke, B. C., & Holmes, M. D. (2003). Aperiodic phase re-setting in scalp EEG of beta-gamma oscillations by state transitions at alpha-theta rates. Hum Brain Mapp, 19 , 248–272. Geman, S., & Geman, D. (1984). Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell , 6 , 721–741. Hamalainen, M., Hari, R., Ilmoniemi, R. J., Knuutila, J., & Lounasmaa, O. V. (1993). Magnetoencephalography - theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev Mod Phys, 65 , 413–497. Kozma, R., Davis, J. J., & Freeman, W. J. (2012). Synchronized minima in ECoG power at frequencies between beta-gamma oscillations disclose cortical singularities in cognition. J Neuroci Neuroeng, 1 , 13–23. Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer.

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Lachaux, J. P., Rodriguez, E., Martinerie, J., & Varela, F. J. (1999). Measuring phase synchrony in brain signals. Hum Brain Mapp, 8 , 194–208. Makeig, S., Westerfield, M., Jung, T. P., Enghoff, S., Townsend, J., Courchesne, E., & Sejnowski, T. J. (2002). Dynamic brain sources of visual evoked responses. Science, 295 , 690–694. Mathewson, K. E., Gratton, G., Fabiani, M., Beck, D. M., & Ro, T. (2009). To see or not to see: Prestimulus alpha phase predicts visual awareness. J Neurosci, 29 , 2725–2732. Mizuhara, H., & Yamaguchi, Y. (2007). Human cortical circuits for central executive function emerge by theta phase synchronization. Neuroimage, 36 , 232–244. Naruse, Y., Matani, A., Hayakawa, T., & Fujimaki, N. (2006). Influence of seamlessness between pre- and poststimulus alpha rhythms on visual evoked potential. Neuroimage, 32 , 1221–1225. Naruse, Y., Takiyama, K., Okada, M., & Murata, T. (2010). Inference in alpha rhythm phase and amplitude modeled on markov random field using belief propagation from electroencephalograms. Phys Rev E , 82 , 011912. Naruse, Y., Takiyama, K., Okada, M., & Umehara, H. (2013). Statistical method for detecting phase shifts in alpha rhythm from human electroencephalogram data. Phys Rev E , 87 , 042708. Palva, S., & Palva, J. M. (2007). New vistas for alpha-frequency band oscillations. Trends Neurosci, 30 , 150–158. 16

Rodriguez, E., George, N., Lachaux, J. P., Martinerie, J., Renault, B., & Varela, F. J. (1999). Perception’s shadow: Long-distance synchronization of human brain activity. Nature, 397 , 430–433. Varela, F., Lachaux, J. P., Rodriguez, E., & Martinerie, J. (2001). The brainweb: Phase synchronization and large-scale integration. Nat Rev Neurosci, 2 , 229–239. Varela, F. J., Toro, A., John, E. R., & Schwartz, E. L. (1981). Perceptual framing and cortical alpha rhythm. Neuropsychologia, 19 , 675–686. Winfree, A. (1987). The Timing of Biological Clocks. New York: W H Freeman & Co.

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A Number of detected phase shifts

22 20 18 16 14 12 10 −0.5 −0.4 −0.3 −0.2 −0.1

0

0.1 0.2 0.3 0.4 0.5

Time (s)

B

Button press

Stimulus onset

Trial 1: Detected trial Detect

150 ms

Undetect Button press

Trial 2: Unetected trial Detect Undetect

Button press

Trial 3: Undetected trial Detect Undetect Button press

Trial 4: Detected trial Detect

Trial N: Detected trial

...

Undetect Button press

Detect Undetect −0.5 −0.4 −0.3 −0.2 −0.1

0

0.1 0.2 0.3 0.4 0.5

Time (s)

Figure 2: A: Number of detedted phase shifts in LA for each time bin. The data were grand-averaged over all subjects. The 0 ms instant on the x-axis indicates the onset of the flash stimulus. B: Definitions of detected and undetected trials. Each row shows the time course indicating whether a phase shift was detected or undetected. Trials in which a phase shift was detected in the 150 ms before the button press were defined as detected trials.

18

Detected trial Undetected trial

*

* Average of z-scored reaction time

**

0.1

0.05

0

−0.05 LA

RA

PA

OA *: p<0.05, **: p<0.001

Figure 3: Averages of z-scored RTs in detected and undetected trials in each area. The error bars indicate the standard errors among the trials.

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Number of detected phase shift

25 LA PA OA

20

15

10

5

0

−0.15

−0.1

−0.05

0

Time (s)

Figure 4: Histograms of the timings at which phase shifts were detected in LA, PA, and OA with respect to the button press (at 0 s).

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