*2.5. Brain Noise Estimation*

The proposed brain noise estimation method is based on phase synchronization, which implies a measurement of a phase difference between the brain's response in the visual cortex and the reference signal at the second harmonic frequency (2 *fm* = 13.33 Hz). First, to obtain the visual response, we averaged the source activity waveforms from the *V*<sup>1</sup> and *V*<sup>2</sup> subregions of the Brodmann atlas for each of the F-trials of a subject. We then bandpass-filtered this average visual response in the 13–14 Hz frequency band. To estimate brain noise, we calculated the phase difference time series between visual response time series and the second harmonic of the flicker sinusoidal signal, as [30,56]:

$$
\Phi = (t\_n^V - t\_n^m) 2f\_{m\prime} \tag{1}
$$

where *t V <sup>n</sup>* and *t m <sup>n</sup>* are the times of *n*th maxima of the visual response time series and the second harmonic of the flicker signal, respectively. Intermittent frequency-locking was observed, superposed with random fluctuations due to phase noise [33]. We also obtained unimodal probability distributions of these phase differences Φ to characterize the phasenoise-induced random fluctuations in phase. Kurtosis, a measure of the sharpness of a unimodal distribution, would be lower for a broader and noisier phase fluctuation distribution, and vice versa. Therefore, from the probability distribution of these random phase fluctuations, we estimated brain noise as the inverse distribution's kurtosis. This method was comprehensively described in the previous paper [30].

## **3. Results**

Based on the obtained normalized distributions of the source power, we calculated for each subject the average power of source activity in the visual cortex, *Davg*, in FieldTrip. It should be noted that we determined the visual cortex using the automated anatomical labeling (AAL) brain atlas [57] in FieldTrip. The average spectral power *Davg* in the visual cortex was plotted in Figure 1 against estimated brain noise to phase synchronization (in units of inverse kurtosis) for every subject.

**Figure 1.** The average power of source activity in the brain volume corresponding to visual cortex versus brain noise for all subjects (numbers denote the subjects). The line is a linear approximation fit (*p* = 0.039, *R*<sup>2</sup> = 0.309).

One can see a linear correlation (with *p*-value equal to 0.039 and an *R*2-value of 0.309) of *Davg* and noise level, although the scatter is significant: *Dmin avg* = 0.04, *Dmax avg* = 1.34; *Noisemin* = 0.22, *Noisemax* = 0.39.

Figure 2 shows typical distributions of normalized source power *D* predominantly activated within the visual cortex for subjects with low (subject 2) and high (subject 6) brain noise. Subject 6 is characterized by more pronounced high-amplitude activity spanning a larger volume in the visual cortex than subject 2.

We will show now the results of the alternate analysis pipeline in Brainstorm. The values of average event-related coherence over visual areas V1 and V2 were compared with the same estimated brain noise as used in Figure 1 for all subjects. A linear relation was established with a *p*-value of 0.048 and an *R*2-value of 0.267, as seen in Figure 3. The distributions of average event-related coherence over the cortex for typical subjects with low and high noise levels are shown in Figure 4 as per the cortical analysis in Brainstorm.

The methodology to calculate the normalized difference of power on a 3D volume in FieldTrip was adapted to fit the 2D source model generated in Brainstorm to have a closer comparison. Figure 5 shows the corresponding linear regression model with a *p*-value of 0.209 and an *R*2-value of 0.118 (*Dmin avg* = 0.08, *Dmax avg* = 2.18; *Noisemin* = 0.22, *Noisemax* = 0.39). Although the model fails to capture any significant relation, the relative positions of the subjects in the power–noise state-space of Figure 5 are quite similar to those which we observe in Figure 1.

**Figure 3.** Average event-related coherence in the visual cortex versus estimated brain noise to phase synchronization. The straight line is a linear regression fit of the data (*p* = 0.048, *R*<sup>2</sup> = 0.267).

**Figure 4.** Typical cortical distributions of event-related coherence for (**A**) Subject 2 (low noise) and (**B**) Subject 6 (high noise). The brain activation is more intensive in the latter case.

**Figure 5.** The average power of source activity in the visual cortex versus brain noise for all subjects (numbers denote the subjects). The line is a linear approximation fit (*p* = 0.209, *R*<sup>2</sup> = 0.118).
