EEG connectivity in functional brain networks supporting visuomotor integration processes in dominant and non-dominant hand movements

Objective. This study explores the changes in the organization of functional brain networks induced by performing a visuomotor integration task, as revealed by noninvasive spontaneous electroencephalographic traces (EEG). Approach. EEG data were acquired during the execution of the Nine Hole Peg Test (NHPT) with the dominant and non-dominant hands in a group of 44 right-handed volunteers. Both spectral analysis and phase-based connectivity analysis were performed in the theta (ϑ), mu ( μ ) and beta (ß) bands. Graph Theoretical Analysis (GTA) was also performed to investigate the topological reorganization induced by motor task execution. Main results. Spectral analysis revealed an increase of frontoparietal ϑ power and a spatially diffused reduction of µ and ß contribution, regardless of the hand used. GTA showed a significant increase in network integration induced by movement performed with the dominant limb compared to baseline in the ϑ band. The µ and ß bands were associated with a reduction in network integration during the NHPT. In the µ rhythm, this result was more evident for the right-hand movement, while in the ß band, results did not show dependence on the laterality. Finally, correlation analysis highlighted an association between frequency-specific topology measures and task performance for both hands. Significance. Our results show that functional brain networks reorganize during visually guided movements in a frequency-dependent manner, differently depending on the hand used (dominant/non dominant).


Introduction
Motor execution is a complex cognitive function that relies on the coordinated activation of spatially close and distant brain regions [1].Specifically, visuomotor integration tasks require the processing and interpretation of visual inputs to plan motor execution and adapt human movements to interact with the environment.The visuomotor integration ability of the brain has been principally explored in functional magnetic resonance imaging (fMRI) studies using protocols involving motor tasks guided by visual cues [2][3][4].A consistent finding is the important role of the frontal and parietal areas in visuomotor integration processes, in addition to the sensorimotor cortex.
For example, the fMRI study by Wolynski et al [2] showed that during a simple button press task triggered by a visual stimulus, both parieto-occipital and motor areas are activated.In [3], it was shown that motor sequence learning involves frontoparietal areas and the magnitude of such activation depends on the complexity of the sequence.Other studies have investigated visuomotor integration processes using functional connectivity analysis, which makes it possible to describe the statistical dependence between the activity of different brain regions and thus to study how they interact and communicate under different conditions [5].Heinzle et al [4], for example, were able to predict visuomotor task difficulty using a classifier based on dynamic functional connectivity analysis, and they suggested that the way brain regions are recruited and communicate changes over time and as a function of task demands.
A Magnetoencephalography and intracranial EEG study [6] investigated brain connectivity in the gamma band and showed that visuomotor processes are supported by a dynamic involvement of parietooccipital and frontoparietal functional networks.Electroencephalography (EEG) based studies confirmed the involvement of frontoparietal areas in visuomotor processes and showed that their activity and interactions are frequency dependent.Croce et al [7] showed that a visually guided force task is supported by a dynamic involvement of both frontoparietal and sensory motor areas, highlighting also different functional roles associated with beta (ß) and theta (ϑ) oscillations.Moreover, Erla et al [8] conducted a functional connectivity study that highlighted the importance of alpha (α) and ß long range interactions between the visual and motor regions during visuomotor integration.The way these distributed brain regions are recruited and organized in functional networks (FNs) can change depending on different factors, such as the type of the executed movement, its complexity, and the state of the subject.
Handedness consists of the preference in terms of use and discrepancy in terms of motor abilities between the two hands, and it could be a factor impacting on the organization of brain networks involved in visuomotor integration.fMRI-based studies, indeed, showed differences in brain activations and functional connectivity between rightand left-handed subjects during the execution of tasks with the dominant and non-dominant hands [9][10][11][12][13].In these studies, the experimental protocol consists in the execution of simple motor tasks, such as finger tapping [9,10], finger-thumb opposition [11] and finger extension [12], which do not involve visual input processing.Results showed the presence of a handedness-dependent hemispheric asymmetry (i.e.greater activation of the brain area contralateral to the dominant hand), which seems to be prominent for right-handed subjects.Moreover, different patterns of brain activation were observed depending on the task repetition frequency [13], and on the type of movement performed [9,11].A few studies have investigated the impact of handedness in terms of brain activation patterns using EEG, mainly highlighting differences in the activation of the two hemispheres between right-and left-handed individuals [14,15].An EEG-based functional connectivity study performed in the ß band on a small group of right-handed individuals also suggested that different patterns of functional interactions may occur during drawing tasks depending on the hand used [16].
In the present work, differently from most existing studies in the field, we evaluated brain electrical activity during the execution of a complex visuomotor integration task, i.e. the Nine Hole Peg Test (NHPT), which requires the continuous processing of visual information to control the performance of fine movements [17,18].Moreover, the current study is the first, to our knowledge, to examine frequency-dependent modulations in brain functions triggered by visuomotor integration processes using spontaneous EEG data from a large dataset, i.e. 44 subjects.The aim of our work was to investigate EEG-based brain networks supporting visuomotor integration tasks performed with the two hands, hypothesising a different efficiency of the network associated with the use of the dominant and nondominant hands.Indeed, we expected that the different experience of using the two hands might result in different organisations of brain networks, which was assessed using the Graph Theoretical Analysis (GTA) [19].
The rest of the work is organized as follows: section 2 provides information about the population, the experimental protocol and the methods adopted for data analysis, while section 3 illustrates the main results obtained from both the spectral and connectivity analysis, with a particular focus on the outcomes from GTA.Finally, results are discussed in section 4 and the main conclusions are summarized in section 5.

Subjects
Forty-four healthy right-handed volunteers (23 males and 21 females, aged between 18 and 30 years old) were enrolled in the present study.None of them had previous impairments affecting the upper limb functions, neither of musculoskeletal nor neurological origin.The experiments were approved by the Ethical Committee of the Humanitas Clinical and Research Center (n.CLF20/08, July 2020) and carried out at the Motion and Posture Analysis Lab and B3Lab of Politecnico di Milano.All volunteers signed an informed consent before the acquisitions, and their privacy was guaranteed by means of personal data anonymization.

Acquisition protocol
The experimental protocol consisted of the following stages: first, EEG data were acquired during one minute of rest with closed eyes, followed by another minute of rest with eyes open.Subsequently, the NHPT [17] was executed with the right and left hands.The NHPT was performed twice for each hand.Data analysis focused exclusively on EEG signals extracted from the resting period with eyes open (i.e.baseline-BL) and on the NHPT execution with both the right (RH) and left hand (LH), corresponding to the fastest performance.The SD LTM 64 express system, designed and produced by Micromed (Mogliano Veneto, Italy), was used for the recording of the EEG signals.These signals were sampled at a sampling rate of 1024 Hz.A total of 55 channels, placed in accordance with the international 10-20 system, were acquired.

EEG pre-processing
EEG pre-processing was carried out by means of the EEGlab MATLAB Toolbox [20].First, raw EEG traces were band-pass filtered in the 1-45 Hz frequency range and resampled at 256 Hz.Then, identification and removal of noisy channels were manually performed.Independent Component Analysis was used to identify and remove artifactual sources [21,22] with the support of ICLABEL plugin [23].Finally, channel re-interpolation and re-referencing to the common average reference were performed.The whole following analysis is represented in the supplementary figure S1 and described in the following sections.

Spectral analysis
The power spectral density of EEG traces was estimated by means of the Welch's method with 1 s window tapering, overlapped by 50%.Within each window, a normalization procedure to bring the signal to zero mean and unitary variance was applied.Then, the variation of power content observed during the execution of the NHPT with respect to a 20second baseline condition with eyes open was computed according to the formula (1): where, P NPHT and P BL are the power spectral densities associated with the NHPT task and the baseline, respectively.The analysis was focused on three different frequency bands: ϑ, individual µ and ß.Specifically, the individual mu (µ) frequency was identified as the frequency bin falling within the standard frequency range between 7 Hz and 13 Hz that showed the greatest reduction in power associated with the dominant hand movement.The final central frequency of the band (µC) was computed as the average of the frequency values identified at the two channels C3 and C4, which are placed on the motor cortex, as illustrated in figure 1.
Then, the individual µ frequency band was selected as the frequency range from (µC−1 Hz) to (µC + 1 Hz).The average individual µ of the population was centered in 11 Hz ± 0.8 std.For the ϑ and ß bands we selected, respectively, the frequency ranges between 4 and 8 Hz and between 14 and 24 Hz, since they do not overlap the µ one.The choice of a lower and less wide ß frequency range with respect to the standard is in line with the literature related to the analysis of EEG during motor actions [24,25].

Connectivity analysis
The pairwise functional connectivity was studied through the Phase Slope Index (PSI ψ ij (f )) [26], which is a measure based on the phase difference between two time series.Specifically, the PSI computation is derived from the imagery part (ℑ) of the coherence between pairs of time series i,j (C ij (f )) according to the relation (2), where δf is the frequency resolution, and F represents the range of frequencies considered.Spectral estimation for coherence computation was performed according to the methods described in paragraph 2.4.Since the Fourier Transform was performed on windows of 1-second length, the frequency resolution δf is equal to 1 Hz.The final connectivity matrix is antisymmetric ( ψ ij = − ψ ij ), introducing, in this way, a directionality information: if ψ ij > 0, the directionality of information flow goes from i to j.

Graphs visualization and analysis
GTA allows to describe a network as a graph, where the graph vertices represent the collection of brain nodes, while the links are the connections between pair of nodes, in our case ψ ij (f ) values.To obtain the graphs for visualization and analysis, the original connectivity matrices were transformed eliminating weak connections and applying a binarization.The procedure is summarized in figure 2.
(1) Group level simplified network (SimN) assessment To investigate network organization within the sample at the group level, we extracted the SimNs, which isolate those connections that are significant for a certain percentage of the subjects among a reduced set of nodes.To this aim, the 55 nodes were grouped into 12 anatomical different brain areas according to table 1 obtaining, for each subject and task, a simplified adjacency matrix 12 × 12.This latter was constructed according to the following procedure: the connectivity from one area-a to another area-b was set to one if there was at least one strong connection (i.e. over threshold) from one of the channels belonging to area-a to at least one of the channels belonging to area-b.In this way, the directionality was maintained.Then a global group level matrix was extracted, for each task and frequency band, by computing a 12 × 12 matrix containing the percentage of occurrence of that connection among all the subjects of our dataset (i.e. if the element between area-a and area-b is equal to 100, it means that for all the subjects that connection is above threshold).A graphical representation of the obtained matrices is depicted in figure 3. Finally, the SimNs were obtained by applying a threshold equal to the 40%, which was considered a reasonable threshold, taking in consideration the inter-subject variability.The SimNs were treated as graphs and used for visualization and interpretation purposes.
(2) GTA Once the transformed (i.e.thresholded and binarized) connectivity matrices were obtained, GTA was performed by means of the Brain Connectivity Toolbox [19].
Using GTA, the following graph measures describing network topology were computed: global efficiency, modularity and degree.The global efficiency (GE) and the degree (D) are two measures of network integration, which consists in the ability of the network to efficiently spread information among spatially distributed nodes.GE is computed for the  whole network as the inverse shortest path length.D, instead, is calculated for each node of the network as the total number of links connected to the node.The modularity (Q) is a global measure of network segregation, which quantifies its tendency to organize in functional clusters of highly interconnected neighboring nodes.
The GTA was carried out both on the total set of 55 electrodes (Total Network), and on subsets of nodes associated to three well-known FNs: the frontoparietal network (FPN), the sensorimotor network (SMN) and the attention network (AN).The association between the EEG channels (i.e.node) and the FNs was based on their probability of measuring the activity of the cortical areas belonging to the FNs, according to the methods introduced in [27] and further detailed in the supplementary material.The final identified FNs are depicted in figure 4. Specifically, GE and D were computed for both the Total Network and the three selected FNs, while Q was not considered for FNs, since it measures how much neighboring nodes tend to organize in clusters, and FNs involve subset of electrodes that are spatially distant.

Statistical analysis
First, a channel-by-channel comparison in terms of power variation was performed between each pair of tasks using a t-test: (i) BL vs RH, (ii) BL vs LH and (iii) RH vs LH.To account for multiple testing, the FDR (False Discovery Rate) method was used to correct the p-values.
To quantitatively compare the results visualized using the SimNs among the tasks, we considered the distribution of percentage values contained in the group level matrices and compared BL, RH and LH with a Friedman test, applying a post hoc Bonferroni correction.
A Friedman's test with post-hoc Bonferroni's correction was also applied to assess differences among the three conditions considered in terms of graph measures (i.e.BL, RH and LH), separately for the Total Network and each FN (i.e.FPN, SMN and AN).Moreover, we investigated if the global measures of integration (GE) and the segregation (Q) of the Total Network were associated with the task performance through the linear Pearson's coefficient (r).Task performance was measured by the execution time, i.e. lower the execution time, better the performance.
The described statistical analysis was performed separately for each frequency bands under study (ϑ, µ, ß).

Power spectral analysis
Figure 5(A) shows the median topographical maps of power variation with respect to a baseline condition (∆P NHPT ) in the ϑ, µ, and ß bands, obtained on our population of 44 healthy volunteers during motor task execution with the two hands.As can be observed in figure 5(A), the two movements show similar trends: an increase in the ϑ contribution and a power decrease in the µ and ß bands.The desynchronization in the µ and ß bands during movement execution is a well-known phenomenon called Event-Related Desynchronization, which is generally prominent on the contralateral sensorimotor areas in the first tens of milliseconds after the motor onset, and then spreads bilaterally [28] over the motor cortex.Concerning node-based statistics, both movements showed a significant (adjusted p-value < 0.05) increase of ϑ power at frontoparietal channels, and a significant (adjusted p-value < 0.05) diffused desynchronization in the µ band (figure 5(B)), with respect to BL.The similarity between the two cases was also confirmed by the channel-by-channel comparison between the righthand movement and the left-hand movement, which, after FDR correction, did not show any significant difference.

Connectivity analysis: group level SimNs
Figure 6 shows the SimN obtained for the three frequency bands to provide a visual representation of the frequency-dependent connections representative of the whole population.The SimN obtained in the ϑ band showed an increase of connectivity for the movement RH compared to BL and the LH movement.The SimN in the µ band for the BL condition was characterized by a dense connectivity.This result indicates that, in resting conditions, most of the subjects present a highly connected µ band network, while during the motor task the number of connections drastically decreased.We can observe that the communication between the central right and central left nodes is present for both movements.In the ß band at rest, the population presented a dense network of significant connections.Conversely, during the motor tasks, the number of significant connections decreased.It can be observed that the network subtended to the dominant hand movement showed more intra-hemispheric connections.The results obtained from the statistical analysis performed on percentage values are shown in figure 7.They quantitatively confirmed what was observed from the SimNs: when comparing RH to BL a significant increase of network connections was observed in the ϑ band, while in the µ and ß bands a significant reduction of connections was observed when comparing BL with both movements (RH and LH).

GTA
Figures 8 and 9 depict the distribution of graph measures in function of the task (BL, RH and LH) and of the frequency bands.Results obtained on the Total Network are displayed in figure 8, while figure 9 reports results from the three FNs.
In the following paragraphs, the detailed descriptions are provided.(1) Total Network (a) ϑ band In the ϑ band, an increase of the average D and of GE was observed passing from BL to RH. if the increase was not statistically significant, it suggests an augmented integration of the network for the dominant hand movement only.This result is consistent with the increase of the displayed connections in the SimN during the right-hand execution.Conversely, the modularity (Q) of the network presented a very similar distribution.
Moreover, a linear relationship between the two global measures Q and GE in the ϑ band with the task performance (i.e.task execution time) was also observed (see figures 8(A) and (B)).Specifically, with the increase of the execution time, an increase of Q and a decrease of GE were observed.This suggests that better performance (i.e.lower execution time) may be associated with greater network integration and lower segregation.The correlations were statistically significant in the LH case, with r = 0.6 (p = 0.002 * 10 × 10 −2 ) for Q and r = −0.4(p = 0.002) for GE (figures 10(A) and (B)).
(b) µ band Statistical analysis detected significant differences in the µ band for D (χ 2 = 10, 13, p < 0.01) and Q (χ 2 = 8, 22, p < 0.05) among the experimental conditions.Specifically, a significant decrease of averaged D was observed both in RH and in LH (p = 0.008 and p = 0.04, respectively).GE followed the same behavior: a decrease was observed during the RH and LH movements with respect to BL, but statistical analysis did not find any significant difference.In both cases, the observed decrease was prominent for the dominant hand movement.These results could be related to the desynchronization of the network and the subsequent reduction of the number of significant connections, as can be seen from the SimNs shown in figure 6.Conversely, Q index significantly increased passing from BL to RH (p = 0.01).These results suggest a movement-related increase in network segregation and a decrease in network integration for the µ (2) FPN (a) ϑ band No significant differences were detected among the three conditions for the graph indexes D and GE.Nevertheless, similarly to the Total network case, an increase of D was observed during RH with respect to BL within the FPN.
(b) µ band A significant difference was detected for D among the analysed conditions (χ 2 = 6, 39, p < 0.05).In this case, D showed a statistically significant decrease only during the RH movement with respect to BL (p = 0.03).GE showed a decrease passing from BL to the motor task execution, but no statistically significant differences emerged.
(c) β band A slight decrease of D and GE was observed during RH movement with respect to BL in the FPN, but no significant differences emerged from the statistical analysis.
(3) SMN (a) ϑ band The ϑ band in the SMN did not show neither significant differences nor distinct trends in terms of network topology among the three different conditions.

(b) µ band
The distributions of the D and GE indexes showed a decrease associated with the RH movement, and significant differences were detected for GE (χ 2 = 6, 04, p < 0.05), which showed a significant decrease during the dominant hand movement with respect to BL (p = 0.04).

(c) β band
No statistically significant differences were detected in terms of topology for the ß band in the SMN.
(4) AN (a) ϑ band Similarly to the Total Network and FPN cases, in the AN ϑ band showed an increase in D and GE during the RH movement with respect to BL, though not statistically significant.
(b) µ band Significant differences were detected for both D (χ 2 = 8, 92, p < 0.05) and GE (χ 2 = 6, 86, p < 0.05) distributions.Specifically, a significant reduction of D was observed for both RH and LH (p = 0.04 and p = 0.02, respectively).In addition, GE significantly decreased only during LH with respect to BL (p = 0.04).This might suggest that the attention network is similarly involved during the task execution both with the dominant and the non-dominant part of the body.
(c) β band Both D and GE decreased passing from BL to the two motor tasks, but this change was not statistically significant.

Frequency-dependent modulations of brain activity
Few studies in the literature have analyzed brain activity during the execution of a non-repetitive and compound motor task, where marked visuomotor integration ability is required during motor performance, such as in sports [29] and drawing [30].Here, we investigated brain processes triggered by the execution of a visuomotor integration task: the NHPT with the dominant and non-dominant hands.The NHPT has been developed to assess manual dexterity in humans and it requires high-level visuomotor coordination skills [17].In fact, unlike a drawing task, the movements must be faster but precise, requiring participants to be focused only on the task and to limit as much as possible unnecessary body movements.Therefore, the NHPT is a suitable motor task to study brain activity behind visuomotor integration functions.
Specifically, the study was focused on the analysis of spectral and connectivity features of continuous EEG recordings in the ϑ, µ and ß bands, during dominant and non-dominant hand movements.Spectral analysis revealed that the motor task elicits, for both hands, an increase in frontoparietal ϑ power and a spatially diffused desynchronization for the µ and ß bands.
These results are in accordance with the literature linking an increase of power in the ϑ rhythm to motor control, especially to motor planning, spatial memory processing and motor learning [7,[31][32][33].ϑ oscillations, indeed, have been largely associated with executive functions involving frontoparietal areas in cognitive processes [34].
Moreover, the desynchronization in the µ and the ß bands associated with motor tasks is a wellknown phenomenon in literature [24].Our spectral analysis results were comparable for the NHPT execution with the dominant and non-dominant hands, suggesting that spectral features might not be sufficient to clearly distinguish the brain mechanisms related to movements executed with the two hands, at least in our dataset.Indeed, we further explored frequency-dependent brain network activity using functional connectivity analysis.Specifically, we started by identifying SimNs extracting functional connections observed in at least 40% of the participants for each specific frequency band and task.This representation was used to shed light on consistent patterns of brain connectivity in the studied population.We observed that the power increase in the ϑ band, observed passing from the BL condition to the movement, was combined with an increment of connections in SimNs, which resulted to be significant only for RH.The desynchronization in the µ and ß bands, instead, was reflected in significantly less connected SimNs during motor execution with respect to BL, for both LH and RH.
Quantitative GTA was used to highlight frequency-and task-dependent differences in network topologies, and brain network topological changes due to laterality.The main differences in network topology were detected in the µ band, which, for movement execution, was characterized by a less connected network, associated with weaker integration (lower D and GE) and higher segregation (higher Q).This behavior was particularly evident for RH in the Total Network, FPN and SMN.Interestingly, this trend was not present in the AN, which showed a similar behavior for RH and LH.A similar but less pronounced behavior was present in the ß band, in which comparable trends were observed for both hands.The ϑ rhythm was, instead, associated with an increase in network integration during RH movement in the Total Network, FPN and AN, though not significant.
These results support the hypothesis that modulations of the activity of these networks vary for the different frequency bands, in terms of network topology.Previous studies in the literature showed that brain networks interactions and network organization depend on the frequency band considered [6][7][8]34].Brovelli and colleagues [6], for example, suggested that, in the high γ band, visuomotor processes are the result of the dynamic interaction and reorganization of functional networks that are also partially overlapped.We also know from literature that brain functions are supported by a balance between integration and segregation [35].Being the present study based on EEG analysis, the modulations of this balance are studied in function of the frequency.The significant increase in modularity (segregation) in the µ band accompanied by an increase in network integration in the ϑ band (though not significant) could represent a different integration/segregation balance modulated by the frequency.
Moreover, it has been shown that the FPN plays a crucial role, together with the SMN, in collecting sensory information and modulating motor actions [6,7,33].It is therefore reasonable that the activity of the FPN and SMN changes depending on the arm dominance and rhythm, as suggested by our results.Here, we may speculate that this difference is associated with higher experience and more efficient motor control associated with movement performed with the dominant hand.The activity of the AN showed a µ modulation during both movements, as NHPT requires the concentration of attentional resources to fine-tune the motor sequence.This modulation seems to not depend on arm dominance, since in our results it was comparable for the two hands.
Interestingly, statistical analysis revealed a positive correlation between Total Network integration in the ϑ and ß bands observed during task execution with the performance: the higher the GE, the lower the time required for task execution and, therefore, the better the performance.The opposite relationship was observed for network segregation measured by the modularity index (Q).Results concerning the ϑ rhythm are in accordance with previous studies in the literature that associated the amplitude of ϑ oscillations with the performance in visuomotor tasks, suggesting that the modulation of this rhythm is involved in coordinating the hand position in space for motor planning and control [7].Considering that the strongest correlations occurred during left-hand movements, we hypothesize that the use of the nondominant hand makes coordinating hand position in response to visual cues more challenging.In addition, the ß band, too, seems to have an important role in the performance of visuomotor tasks.In fact, it has been linked to the ability of focusing the attention on useful sensory input for movement control, thereby inhibiting the processing of unnecessary information [7,8,36].These results suggest that ß and ϑ activity have a critical role in the fine control of movements requiring visual integration and that an increased and efficient communication among distributed brain areas support visuomotor functions.

Methodological discussion
Some considerations on the methodologies adopted in the present work should be done.Since scalp EEG records brain electrical activity collecting a mixture of contributions from multiple brain structures, the volume conduction (VC) problem is introduced, with the consequent risk of detecting spurious brain connectivity links.For this reason, we adopted the PSI for our analysis: the use of the slope for connectivity estimation, indeed, allows to be robust against VC confounds, since the cases in which the phase difference between the considered time series is zero (and, therefore, the time delay is null) are neglected.Nevertheless, we are aware that the potential confounds due to VC are not completely removed with this approach.An alternative method for VC reduction could have been the source reconstruction procedure.Nevertheless, this latter requires the resolution of the ill-posed inverse problem, for which some physiological assumptions must be done, reliably affecting the final results [37,38].We therefore decided to conduct both connectivity analysis and GTA working at the sensor level to meet a good tradeoff between results interpretability and simplicity of the proposed pipeline for brain networks investigation.In our analysis, we adopted a valuable association method which, bypassing the resolution of the inverse problem, allowed us to meaningfully select and aggregate EEG sensors in a simplified way for GTA, which is generally conducted in the literature merging the contribution of the electrodes of the whole network or of arbitrary defined anatomical brain areas.

Limitations of the study and future works
Obtained results introduced new insights for brain functions modulations induced by visuomotor integration processes, which are expressed and can be studied in terms of frequency-dependent changes in networks topology.Nevertheless, caution is needed in generalizing our results, since further investigations are necessary to fully understand the subtended physiological processes.For example, our dataset included right-handed volunteers, but similar investigations in left-handed volunteers and patients affected by neurological disorders could provide a broader perspective in terms of physiological and methodological understanding.Indeed, neurological disorders alter the communication characteristics among brain regions, affecting also functional interactions [39,40].Moreover, evidence suggests that right-handed and left-handed individuals may present different brain functional strategies for motor execution [9][10][11][12][13].
For this reason, it would be beneficial to investigate how our approach could provide different results under different scenarios.This would provide further evidence on the usefulness of the network descriptors adopted in this work and lead to the identification of potential biomarkers for evaluating neurophysiological correlates of behavioral effects induced by neurorehabilitation techniques in subjects with motor and functional impairments.

Conclusions
The present work enriched the existent knowledge about frequency-specific modulation of brain network organization changes associated with visuomotor integration processes, also in function of the arm dominance.It also demonstrated that, starting from spontaneous EEG signals, the comprehensive use of connectivity and graph analysis can highlight different network organization patterns depending on the rhythm, functional network type, and laterality.Moreover, frequency-specific network measures correlated with task performance for both hands.These findings contribute to understanding brain network changes during visuomotor tasks in right-handed volunteers.Moreover, the use in the future of such brain networks descriptors could offer new insights for motor rehabilitation and training strategies.

Figure 1 .
Figure 1.Procedure adopted for the identification of µC: it is computed as the average of the two frequencies at which the minimum peak of P NHPT − PBL is found in C3 (left panel) and in C4 (right panel).The two plots also show the trend of the power spectral density of the baseline (PBL) and the power spectral density observed during the motor task P NHPT , again at C3 and C4 level.

Figure 2 .
Figure 2.Procedure followed for connectivity matrices preparation to following analysis.As a first step, original PSI measures are calculated (A); The connectivity measures that were, in absolute value, below a certain threshold were eliminated, in order to keep only the strongest connections (B).This threshold was determined, for each subject and frequency band, considering the 95th percentile of the distribution of all the PSI values obtained for the three tested conditions.Then, matrices were further processed through the removal of negative values (C), which provide redundant information, and finally they were made binary (D).

Figure 3 .
Figure 3.An example of group level matrices in the µ band computed for the BL, RH and LH conditions.Color code and values represent the percentage of participants showing a valid connection between the linked areas.

Figure 5 .
Figure 5. (A) Median topographical maps of ∆P NHPT in the ϑ, µ and ß bands during RH and LH movements.Positive values identify power increase, while negative ones identify power decrease with respect to the baseline.(B) Maps of adjusted p-values obtained in the t-test at each channel comparing the RH and LH movements with the baseline in the ϑ, µ and ß bands.Electrodes showing a significant increase of power are highlighted in red, while electrodes showing a significant desynchronization are highlighted in light blue.

Figure 6 .
Figure 6.Simplified networks (SimNs) obtained for the ϑ, µ and ß bands in the three analyzed cases BL, RH and LH.Arrows represent the connections that were significant for at least the 40% of the population.

Figure 7 .
Figure 7. Distribution of the percentage values contained in the group level matrices associated with the different tasks (BL-red, RH-green LH-blue) and frequency bands considered (ϑ, µ and ß).Each value in the boxplot represents a cell of the group level matrices.* Indicates statistically significant difference between task pairs (p < 0.05).

Figure 8 .
Figure 8. Distributions of D, GE and Q computed on the Total Network for the ϑ, µ and ß bands during the BL (purple), RH (blue) and LH (red) phases.The dots in the box plot represent each participant's individual index value.* indicates significant differences (corrected p-value < 0.05).

Figure 9 .
Figure 9. Distributions of D and GE obtained in the ϑ, µ and ß bands in the three FNs considered (from top to bottom: frontoparietal network, sensorimotor network and attention network).The dots in the box plot represent each participant's individual index value.* indicates significant differences (corrected p-value <0.05).

Figure 10 .
Figure 10.Scatter plots and regression lines depicting how Q and GE in the ϑ band vary with execution time separately across subjects for the RH movement (right panel) and the LH movement (left panel).

Table 1 .
List of the twelve identified brain regions and the associated electrodes.