Abnormal Low-Gamma Small-World Response After Visual Stimulation in Schizophrenia

Schizophrenia can be described as a functional dysconnectivity syndrome that affects the brain’s circuits in a generalized way. Global disconnection in schizophrenia has been manifold described by applying graph theory and quantifying parameters of network connectivity. However, little is known about how sensory stimulation modulates networks in schizophrenia, such as small-worldness during visual processing. In order to address this question, we applied graph theory algorithms to EEG recordings and classied the functional network in the alpha (8–13 Hz) and low-gamma (36–55 Hz) bands of 13 patients with schizophrenia (SCZ) and 13 healthy controls (HC) during the presentation of a visual stimulus. We measured the amplitude of visual-evoked potentials and the number of nodes, edges, mean degree centrality, clustering coecient, characteristic path length (L), and small-worldness (SW). As expected, patients presented smaller peak amplitudes of evoked-potentials than HC. Interestingly, in contrast to the controls, SCZ did not change their small worldness index during visual stimulation. This implies that schizophrenia-related dysconnectivity has an impact on the ability of the low-gamma network to react to new sensory input. These results provide evidence about a possible electrophysiological signature of the global decits revealed by the application of graph theory onto the EEG in schizophrenia.


Introduction
Scientists have spent several decades trying to establish a biochemical marker that assists in the The small-worldness (SW) stood out from the multitude of graph-extracted parameters quantifying brain network properties (e.g. centrality, betweenness, resiliency, synchronizability, and modularity), because its characteristics allows to approximate an ideal brain structure as one which would exhibit both local a cost-e cient SW-oriented response (BAEK; PARK; PAIK, 2020). Though they very likely exist, small world patterns have not yet been described for EEG activity obtained during visual processing. Therefore, in order to analyze the parameters of global functional connectivity related to visual perception in healthy subjects and patients with schizophrenia, we recorded pattern-reversal visual evoked potentials and quanti ed the graph-based network measures.

Pattern-Reversal Visual Evoked Potential (PR-VEP)
We measured the amplitude and latency of PR-VEP for each of the stimulus onset (P1a and P1b, see methods) for the occipital electrodes (O1, Oz and O2) and compared them between the two groups: healthy controls (HC) and patients diagnosed with schizophrenia (SCZ). Our result indicates that the amplitude of the PR-VEP is affected globally in SCZ for all occipital electrodes ( Figure 2 On the other hand, the PR-VEP latencies behave similarly between SCZ and HC groups for P1a and P1b (p > 0.05) suggesting that only time-lagged electrophysiological patterns involved in occipital activity during visual stimulation may be largely preserved in SCZ.

Graph-based Network Measures
In order to characterize the connectivity at different coherence scales, we calculated the graph-based Magnitude-Squared Coherence (see methods, MSC) matrices for alpha (8-12 Hz) and low-gamma (36-55 Hz) bands for two different thresholds, either the centroid average (Centroid-based Network, CBN) or a MSC score higher than 0.65 (Threshold-based network, TBN, see methods) considering only pairwise values which cross the respective threshold for the calculation of graph measures. Whereas CBN emphasizes those phase-connections close to the average value of the entire network, and TBN networks keep only those elevated (and less frequent) connections. In Figure 3, example connectivity matrices for the low-gamma coherence are illustrated for both a healthy control (A) and a patient (B). From each connectivity matrix, we measure the number of nodes, number of edges, mean degree centrality (MK), mean clustering coe cient (MC), characteristic path length (L) and small-worldness (SW). The statistical signi cance for each threshold and frequency intervals are presented in the subsections below.

Low-gamma networks
In the low-gamma band, differences between pre-stimulus and VEP epoch are signi cant for all analyzed network properties for the TBN threshold (p < 0.01, Figure 4A-F), but only for characteristic path length (L) and small worldness (SW) in the LBC network ( Figure 4E, F). Surprisingly, we observe that both these measures differ between healthy controls and patients with schizophrenia ( Figure 4E Figure 5F), but none of the remaining graph measures (Fig. 4A -D).
In contrast, all graph measures were signi cantly modulated by stimulus-onset ( Figure  We computed the evoked CBN graph and compared the same network measures between groups and frequency bands to describe the role of speci c evoked edges after the visual stimulus. In the evoked network in the alpha band ( Figure 6A), the number of edges of SCZ patients was lower (median = 103; SD = 14.26) than that of HC subjects (median = 118; SD = 11.84). A Mann-Whitney test indicated that this difference was statistically different (U = 43; p = 0.03). The mean degree centrality of SCZ patients was also lower (median = 6.96; SD = 0.92) than that of HC subjects (median = 7.86; SD = 0.75). This difference was con rmed by the Mann-Whitney test (U = 42; p = 0.02). However, no difference was observed between groups for mean clustering coe cients (U = 81; p = 0.87), characteristic path length (U = 67.5; p = 0.39), and small-worldness (U = 70; p = 0.47).
This could indicate that MSC networks of SCZ patients are impaired to reach large distances, speci cally for frequencies in the low gamma band. In order to represent the behavior of those networks in a topographically manner, we illustrate the evoked CBN graph networks of one subject of each group according to the 10/20-electrode placement for alpha and low-gamma in Figure 6CD, respectively.

Discussion
We recorded topographic EEG signals driven by a full contrast visual stimulation using pattern reversal checkerboards and analyzed graph-based properties of Magnitude-Squared Coherences of the visualevoked potentials in patients with SCZ and HC. We found characteristic network differences between resting state activity and visual evoked potentials in both healthy control and patients as quanti ed from medium phase coherence networks during both phases, suggesting that visual input modulates the cortical network during visual stimulation regardless of the group. However, our results also indicate that, during visual stimulation, topographic cortical integration in the low-gamma band (36-55 Hz), as measured by L and SW values is speci cally impaired in SCZ patients. However, due to their local nature, the well-described de cits in the visual pathways of patients with SCZ are not directly in line with the disconnection theory about the schizophrenic brain. Moreover, our study is the rst to describe not only the known amplitude differences in EEG recordings, but also the dynamic interactions between different recording sites using phase connectivity measures during visualization of the stimulus. Our results indicate that a PR-VEP stimulus modi es network properties (number of nodes and edges, mean degree centrality, clustering, characteristic path length and small-worldness) in patients with schizophrenia and healthy volunteers in both frequency bands when compared with pre-stimulus activity (PSI).
In contrast to healthy HC volunteers, the pattern reversal visual stimulus does neither increase smallworldness nor the characteristic path length for EEG responses in the low-gamma band of patients with SCZ. In detail, our visual stimulus paradigm drives an increase of small-worldness in HC subjects. This suggests that under healthy conditions visual input changes the phase network organization (VEP epoch) when compared to the pre-stimulus activity (PSI epoch), in a characteristic manner. Visual inputs seem to increase the randomicity of the complex network and the organization of the edges involved in stimulus processing creating a more random network (characterized by a highly clustered network with reduced characteristic path length, See Figure 1). The same stimulus does not evoke as many new edges in patients as in healthy subjects, as illustrated in Figure 6CD, and the stimulus-induced increase in randomicity is lacking. Therefore, the hypothesis stands to reason that this inability to alter the low-gamma network according to new sensory inputs -especially in response to a high-contrast visual stimulus -could be one of the manifestations of the disconnection syndrome in psychosis.
The reduced small-world phenomenon supporting dysconnectivity in schizophrenia is mostly described as a feature of structural networks estimated from MRI or fMRI recordings at rest or during a cognitive task. Lynall et al. (2010), for instance, showed substantial reductions in clustering, small-worldness and the probability of high degree hubs in SCZ patients. But these structural in uences in the characteristic path length and clustering coe cient in psychosis are not only derived from the neuronal bers themselves, but also from the local cortical thickness, as shown by ZHANG et al., (2012), for example.
The reduction of the small-world network towards greater global regularity in schizophrenia (see Fig. 1 2018) is the only study that investigates the EEG network responding to a certain sensory stimulus -in this case, an auditory P300 oddball task. Corroborating with our main nding, they found a decrease in characteristic path length in the theta band exposed by the auditory task. Interestingly, in their pioneer study Uhlhaas and colleagues (2006) analyzed long-range synchrony through phase-locking during Gestalt perception and described that speci c Gestalt de cits in schizophrenia were associated with a loss of beta, rather than gamma, phase synchrony, but, in general, reduced gamma band synchronization indicating impaired Our study is limited by the sample size, the number of trials during the PR-VEP, and the polymedicated SCZ sample. It is known that, in addition to the de cits caused by the disorder itself, different antipsychotics might not only alter the visual perception (FERNANDES et al., 2019A; FERNANDES et al., 2019B), but lead to substantial changes in the overall functional network organization of SCZ patients (HADLEY et al., 2016). Thus, in future studies, we intend to assess the network expressed in graphs in a larger and homogeneously medicated sample of patients, and with a higher number of EEG electrodes.
Our work is the rst to show that visual stimuli alter the small-world network response in patients with schizophrenia, and various visual stimuli designed to isolate the different pathways in the visual system, such as the parvo-and koniocellular pathways, have yet to be explored.
We may conclude that phase-dependent functional connections, speci cally in the low-gamma band, react less to visual input in patients with schizophrenia than in healthy conditions, indicating that functional networks in schizophrenia may be denser and thus do not allow greater cortical integration, resulting in the absence of a stimulus-induced small-world response.

Participants
All procedures were performed in compliance with the ethical principles of the Declaration of Helsinki, and were approved by the Research Ethics Committee of the Federal University of Paraíba (Registration number: 45774715.9.0000.5188). The Informed consent was obtained from all the volunteers. Twentythree volunteers participated in the study, 13 diagnosed with schizophrenia according to 10th International Classi cation of Diseases (SCZ group; mean age = 38.3 years; SD = 9.61 years) and 13 healthy controls (HC group; mean age = 28.92 years; SD = 12.92 years) with no psychiatry in rst and second-degree relatives. SCZ patients were recruited at the local Psychosocial Care Center. All participants had normal or corrected-to-normal (20/20) visual acuity (Raskin E Optotypes) and no color blindness (Ishihara's Test) (CLARK, 1924). Further, they had no history of drug abuse, brain trauma, diabetes, heart disease and neurological or psychiatric disorders (except for the SCZ group). Table 1 presents the sociodemographic characteristics of the samples divided according to the type of antipsychotic used in the latest 6 months before data recordings.

Pattern-reversal Visual Evoked Potential -PR-VEP
Visual stimuli were presented in pairs of phase-reversing checkerboards and consisted of 11 x 11 arrays of checks at maximum contrast, on a gray background with approximately 30 cd/m² of luminance. A block of 49 pattern-reversals was presented on a 20' monitor at a 150 cm distance from the subjects.
Each pattern was presented for 120 ms, with intervals of 800 ms (Figure 7). Participants were instructed to keep their eyes xed at the center point of the screen until the task was completed (approximately one minute) and avoid excessive body movement, blinks, lateral eye movements, and biting.

EEG recording and preprocessing
During presentation of pattern reversals, the EEG was recorded using a 32 active channel system (actiCHamp, Brain Products, Herrsching, Germany) with DC recording sampled at 500 Hz and impedances below 10 kΩ (kilo ohms) per electrode during all experiment sessions. The electrodes were connected to an air-permeable cap with adjustable size to the participant's head (Easy-cap, Herrsching, Germany) using a spatial distribution following the international 10/10 system (JURCAK; TSUZUKI; DAN, 2007) We applied saline gel (SuperVisc, EasyCap GmbH, Herrsching, Germany) to facilitate signal transduction and promote the correct electrode contact. After the recording section, data were re-referenced by common-average, band-passed using a Butterworth lter of order 2 between 0.6 and 100 Hz. The artifacts were removed through a semiautomatic Independent Component Analysis using ICLabel (PION-TONACHINI; KREUTZ-DELGADO; MAKEIG, 2019). After the preprocessing step, the data was visually inspected and imported to MATLAB to perform the analysis of the visual evoked potential and graphbased connectivity.

PR-VEP analysis
After identifying the stimulus onset per trial using the photo sensor data, EEG time-series data were windowed into valid segments of 700 ms (100 ms of PSI activity and 200 ms of VEP) only on the occipital electrodes (O1, Oz and O2) and identi ed the amplitude and latencies of P1a and P1b components per trial, referring to the rst and second checkerboard visual responses, respectively. For each subject, all amplitude and latencies were then concatenated and averaged.

Connectivity measures and graph analysis
We measured the Magnitude-Squared Coherence (MSC) (Equation 1) for the alpha (8 -13 Hz) and lowgamma (36-55 Hz) band to estimate the bidirectional coupling across functional phase connectivity among all pairs of electrodes and measured during PSI and VEP using the function mscohere. The MSC estimates the phase coupling between x and y signals at a frequency (f) by measuring the squared magnitude of the complex cross power spectral density (Pxy) divided by the auto-spectral densities (Pxx) and (Pyy). For PSI, we calculated the MSC 200 ms before the stimulus onset with a 100 ms Hamming window with 50% overlap, while for the VEP coherence we used a 200 ms Hamming window with 50% overlap. It resulted in adjacency matrices per each trial/condition (PSI and VEP) and groups (HC and SCZ). We then set two thresholds to measure the network at different points of view: 1) the centroidbased Network (CBN) which considers only MSC +/-0.5 standard deviation of the average MSC to provide the graph-based analysis of the mean subject-to-subject phase synchrony. 2) the threshold-based network (TBN) which considers only MSC higher than 0.65 and below 1 to estimate the phase synchrony at elevated coherences. The TBN network represents a rare network present throughout the connectivity matrix, since it is derived from a limit that removes more substantial nodes and edges below the de ned value, leaving only the highest MSC values that may not fully represent the network during visual activity. Thus, TBN networks tend to exhibit fewer nodes and edges, but highly connected functional networks (BORDIER ET AL., 2017). Where k i are all connected neighbors to node i and t i is the number of links between them.
The small-worldness is a measure of randomness, which is calculated by normalizing the ratio of the clustering coe cient (C) and the characteristic path length (L) by the same measurements for a sizematched random network (WATTS; STROGATZ, 1998): Statistical analysis All statistical analysis was performed using IBM SPSS 26.0. Descriptive analysis is reported as means and standard deviations for the sociodemographic and amplitude and latency VEP measures, while means and standard error of the mean were used to describe the graph-based estimations, due to their sample size. Group differences (HC and SCZ) were measured using a non-parametric test for PR-VEP analysis (Mann-Whitney Test), and parametric Two-way repeated-measures ANOVA were applied to estimate the stimulus, group or Group x Stimulus main effect on the network measures. Statistical differences were considered if p-value was ≤ 0.05. Yet, due to the sample size of the graph estimates, we also consider the effect size (partial eta squared ²p) ≥ 0.4 as a criterion for signi cance.   Figure 1 The level of randomness of a network expressed by the Clustering coe cient (C) and the Characteristic Path Length (L). Three network types de ned by their nodes and edge boundaries. A regular network shows higher C and L indexes, a small-world network has high C and low L indexes (many short distance node-to-node connections and few long connections). The graph below demonstrates how randomness increases steadily with the decay of L and subsequently C indexes. Finally, the random network exhibits the same probability of short and long node-to-node connections (both low C and L indexes). Non-parametric Mann-Whitney signi cance: * (p < 0.01) for paired comparisons between HC and SCZ groups.     Example of one trial of the pattern-reversal visual evoked potential paradigm. Each trial started with a prestimulus interval (PSI) containing a xation point at the center of the screen for 800 ms, followed by two reversal checkerboard patterns with maximum contrast for 120 ms each pattern (VEP). Each trial lasted 1040 ms and was repeated 49 times for all volunteers.