**1. Introduction**

The human brain is a complex network consisting of approximately 86 billion neurons [1] subdivided into oscillatory clusters that fire co-dependently/independently to manifest our consciousness as we know it. These clusters correspond to regions of the brain specialized in processing certain types of information and are connected to other specialized regions in complex networks.

Brain connectivity is studied in three forms: functional, structural, and effective [2–5]. Structural connectivity identifies anatomical neural networks that show possible pathways for neural communication [6,7]. Functional connectivity finds active brain regions that have a correlated frequency, phase, and/or amplitude [8]. Effective connectivity utilizes the functional connectivity information and additionally determines the direction of the dynamic information flow [9,10]. Effective and functional connectivity can be measured in the frequency domain (e.g., coherence [11]) and in the time domain (e.g., Granger causality [5] or artificial neuronal network-based functional connectivity [12]).

Inter-neuronal communication is realized by one of 50+ neurotransmitters that can be either excitatory (e.g., dopamine) or inhibitory (e.g., gamma-Aminobutyric acid (GABA)) [13]. Voltage-gated ion channels on the cell membranes of neurons generate action potentials and periodic membrane potential activity that synchronizes neighboring neurons [14,15]. These neighboring neurons may, in turn, affect other remotely located neurons, creating a network of connectivity. Coherence-based neuronal communications are driven by the dynamics of neurotransmitters such as amino acid glutamate and GABA.

Only when the synchronous neuronal population is large enough, the produced electrical activity and the concomitant magnetic activity is strong enough to be detected outside

**Citation:** Chholak, P.; Kurkin, S.A.; Hramov, A.E.; Pisarchik, A.N. Event-Related Coherence in Visual Cortex and Brain Noise: An MEG Study. *Appl. Sci.* **2021**, *11*, 375. https://doi.org/10.3390/app11010375

Received: 12 November 2020 Accepted: 30 December 2020 Published: 2 January 2021

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the skull using methods such as electroencephalography (EEG) and magnetoencephalography (MEG), respectively [16]. MEG measures the ionic currents inside the neuron (primary currents), whereas EEG measures the return or volume currents outside the neuron (secondary currents).

Coherence is commonly used to quantify neuronal synchronicity between spatially separated EEG electrodes or MEG coils [17]. It is essentially an estimate of the consistency of the relative amplitude and phase between two signals within a given frequency band. There is a linear mathematical method resulting in a symmetric matrix, lacking any directional information. Identical signals produce a coherence magnitude of 1, whereas the coherence magnitude approaches 0 as the dissimilarity between the considered signals increases.

In the last two decades, significant progress has been achieved in the development of new computational algorithms that enable connectivity calculations directly between the different regions of the brain (source space) [5] instead of electrodes or coils (channel space). The source space analysis provides better anatomical localization [18] and enables inter-subject or group analysis as the brain activity now can be projected onto a more standardized space.

In 2004, Hoechstetter et al. [19] introduced a new method to study source coherence in the brain. Discrete multiple source models were created using brain electrical source analysis, and the source activity was transformed into time–frequency space. Finally, magnitude-squared coherence was evaluated to reveal coupled brain sources. The application of inverse solutions to estimate brain activity in the source space from the channel space removes current leakage among adjacent channels. This averts localization errors that are fundamental to coherence analysis in the channel space [19].

Coherence has henceforth been used in many brain connectivity studies on patients and healthy subjects, including but not limited to studies on working memory [20], brain lesions [21], hemiparesis [22], resting-state networks [23], schizophrenia [24–26], favorable responses to panic medications [27], and motor imagery [28,29].

Owing to the diversity of human brains, we observe various forms of coherent neuronal activity over different subjects in response to the same flickering stimulus. For example, the presentation of flickering visual stimuli instils coherent responses in the visual cortex at the flicker frequency and its harmonics with varying coherent neuronal network sizes among the subjects [30,31].

Another signal processing technique used to measure synchronization in EEG and MEG is phase synchronization, a measure of how stable the phase difference is over the considered time duration. Phase synchronization requires considered signals to be phaselocked with zero or any finite phase difference, regardless of their respective amplitudes. This is in contrast to the coherence measurement in which phase and amplitude are intertwined for its estimation [32].

Noise, as known [33], can cause desynchronization in a neuronal network. Each participating neuron and interconnecting synapses add to the inherent brain noise when a stimulus is presented to the subject. Therefore, one could argue that a larger neuronal network would carry a higher brain noise and, consequently, lower average coherence. On the other hand, larger active neuronal oscillations in response to the stimulus are likely to have stronger average coherent activity and would also entail higher brain noise. Thus, the relation between the observed coherence and the level of inherent brain noise remains unclear and is the central problem explored in this paper (for comprehensive theoretical descriptions, see [34,35]).

Recently, an approach to estimate inherent brain noise based on phase synchronization was proposed [30]. The method is based on the experiments with flickering images and simultaneous recording of magnetoencephalographic (MEG) data. This paper utilizes the same methodology to measure brain noise using the same experimental paradigm and reveal its correlation with the induced coherence or source power in the visual cortex. We deal with the two most popular open-source MATLAB toolboxes for MEG data analysis, namely FieldTrip [36] and Brainstorm [37], to perform two independent analyses that are more suitable to each software.

#### **2. Materials and Methods**

We carried out MEG experiments based on the flickering paradigm with 17 conditionally healthy subjects (age: 17–64 years; 10 males) with normal or corrected-to-normal visual acuity. Two subjects were later discarded. Frequency tags at the stimulus frequency and its harmonics were absent in subject "sub08", perhaps due to a lack of focus on the experiment. Meanwhile, for subject "sub11", the ECG activity was not recorded during the experiment due to a technical error, and therefore the signal-to-noise ratio of the subsequently cleaned data was too low to allow correct data analysis. All subjects provided written informed consent before the experiment commencement. The experiments were performed as per the Declaration of Helsinki and approved by the Ethics Committee of the Technical University of Madrid.

#### *2.1. MEG Acquisition*

MEG recordings were performed with an Elekta-Neuromag system with 306 channels that was housed in a magnetically shielded room at the Centro de Tecnología Biomédica, Universidad Politécnica de Madrid. The head position was continuously tracked with head position indicator (HPI) coils and co-registered in the device and head coordinate system with three fiducial points (nasion, left, and right preauricular points) and around 300 scalp surface points digitized by a Polhemus Fastrak system. A vertical electrooculogram (EOG) and electrocardiogram (ECG) were placed to capture eye blinks and cardiac activity, respectively. The data were sampled at 1000 Hz.

The experiments for all 17 subjects lasted 4 days. Along with MEG recordings of the subjects, the MEG data were also collected daily in an empty room. All data were passed through an online anti-alias bandpass (0.1–330)-Hz filter. MaxFilter software was used for the temporal signal-space separation (tSSS) to reduce magnetic interference and perform head movement compensation. A 56-ms delay between event triggers and the actual stimulus was measured separately using a photodiode.
