Functional Connectivity in Developmental Dyslexia during Speed Discrimination

A universal signature of developmental dyslexia is literacy acquisition impairments. Besides, dyslexia may be related to deficits in selective spatial attention, in the sensitivity to global visual motion, speed processing, oculomotor coordination, and integration of auditory and visual information. Whether motion-sensitive brain areas of children with dyslexia can recognize different speeds of expanded optic flow and segregate the slow-speed from high-speed contrast of motion was a main question of the study. A combined event-related EEG experiment with optic flow visual stimulation and functional frequency-based graph approach (small-world propensity φ) were applied to research the responsiveness of areas, which are sensitive to motion, and also distinguish slow/fast -motion conditions on three groups of children: controls, untrained (pre-D) and trained dyslexics (post-D) with visual intervention programs. Lower φ at θ, α, γ1-frequencies (low-speed contrast) for controls than other groups represent that the networks rewire, expressed at β frequencies (both speed contrasts) in the post-D, whose network was most segregated. Functional connectivity nodes have not existed in pre-D at dorsal medial temporal area MT+/V5 (middle, superior temporal gyri), left-hemispheric middle occipital gyrus/visual V2, ventral occipitotemporal (fusiform gyrus/visual V4), ventral intraparietal (supramarginal, angular gyri), derived from θ-frequency network for both conditions. After visual training, compensatory mechanisms appeared to implicate/regain these brain areas in the left hemisphere through plasticity across extended brain networks. Specifically, for high-speed contrast, the nodes were observed in pre-D (θ-frequency) and post-D (β2-frequency) relative to controls in hyperactivity of the right dorsolateral prefrontal cortex, which might account for the attentional network and oculomotor control impairments in developmental dyslexia.


Introduction
Developmental dyslexia is defined when poor reading is accompanied by normal intelligence, adequate education, and a lack of other psychologically important factors [1]. Visual processing in developmental dyslexia is the main area of this study. The relatively poor performance of dyslexics in motion processing tests [2,3] is evidence of a major deficiency in visual processing in dyslexia [4,5]. The shortcoming in the differentiation of speeds [6,7] is selectively related to the velocity factor on reading sub-skills, characterized by fluency and reading speed [8], but does not correlate with any measures for their accuracy, presuming that this deficit results neither from dysfunctions in visual nor from those in the attentional system in developmental dyslexia [9]. In this debut, the question still remains whether deficiencies in the processing of visual motion in dyslexia are specific to motion or are resulted from dysfunctions in the visual or attention systems [10]. Various visual attention deficits in dyslexia include difficulties in tasks with serial search [11][12][13], attentional orientation with a peripheral cue [14], or suppressed peripheral visual information [15], selective attention [16,17], and attentional focusing [18]. While reading, the combining of identified letters in the appropriate sequence forms words using the cir-and their children agreed to participate in an EEG study after signing an informed consent according to the Helsinki Declaration. The research was approved by the Ethics Committee of Institute of Neurobiology and Institute for Population and Human Studies, BAS (No. 41/12-07-2019), and the Ministry of Education and Science (No. 09-69/28-03-2017). The schoolchildren pass through neuropsychological tests [59]. Psychological test battery DDE-2 was applied to examine developmental dyslexia [60,61]. Psychometric tests were used to assess reading, writing skills and phonological awareness [62]. For the children with learning difficulties, not only the Raven test for nonverbal intelligence "Progressive Matrices" [63] but also the Girolami-Boulinier test for non-verbal perception "Differently Oriented Marks" [64,65] was applied.

Experimental Paradigm
This visual motion paradigm was radially moving flow fields, the expansion of each appears in pair with a referent speed and a different speed. The duration of each stimulus (flow) in a pair was relatively short 300 ms with abrupt onset/offset and an interval of 500 ms between two compared stimuli in a pair. Every pair set was interleaved with a pseudo-random gap to 1.2-2.5 s between them, so the bias of the neural response is minimized due to the brisk on-off switch of the flows. The stimulus duration of 300 ms was sufficient to achieve both the strong reaction to visual stimulus and to reduce spontaneous eye movements during a stimulus presentation. There were no constraints on maintaining fixation while viewing flows to have a more natural visual experience as possible. The approach was a classical formulation of flow fields with more explicitly denoising of surfaces, boundaries, and the flow field motion over time by median filtering [66]. To improving accuracy, a median filtering step applies after every warping step within coarse to fine estimation in the incremental process of flow. The algorithm with first ranks in both endpoint and angular errors optimizes its objectives through a medium step of filtering. The flow is regulated in a big spatial neighborhood adaptively in a further expanding region. The filter is used between the values in the flow intermediately during the warping on all pixels. Fewer iterations are applied without reusing the results of sorting adjacent pixels. This procedure significantly reduces computational costs. There is a small loss of performance on small-scale motion sequences. Two terms are combined for small, fastmoving objects. The permanent term is about some constant property of the image. An expected variability of the flow in the image at large displacement is modeled by a spatial term. A set of parameters as speed and direction were estimated from the movie frames with the assumption that the neighboring blocks share a similar motion since the motion in a frame is coherent [67].
The requirement in speed discrimination was to identify a faster extended optical flow in two successive stimuli. In the fine velocity discrimination, the velocity discrimination stimuli in the pair moved at 4.5 • /s vs. a reference speed of 4.0 • /s. In the coarse condition, the velocity discrimination stimuli moved at 5.0 • /s vs. the reference speed, defined in a previous psychophysical procedure [9,68,69]. Speed identification is one particular instance of speed discrimination. The second term in the couple after the referent one is used for two types of speed discriminations. The speed differences were 0.5 and 1 to the reference. The task was performed in a darkened room. The presentation of white optical flows was centrally in the visual field on a black screen (Alienware 17.3-inch FHD with resolution 1920 by 1080 pixels with a pixel pitch of 0.1989 mm, 60 Hz refresh rate). Generation of stimuli was performed by in-house development Matlab script (Mathworks, Inc., Natick, MA, USA) on NVIDIA GeForce GTX 1080 graphics card. All stimuli were expanded radial optic flows [67] with a circular eccentricity of 14 • from the fixation point with an average luminance of 50 cd/m 2 . The viewing was binocular at a distance of 57 cm to the screen. In the velocity discrimination, the speed was judged from children by a left or right response key for fast speed than a reference or slow. The children respond after the second stimulusoff with the right thumb each time when they see flow with similar velocity to the reference one. They press another button with the left thumb each time when a faster flow appears after the reference one in the pair. As their attention is kept high during the experiment, a period of 500 ms after the second flow-off is included in the analysis. For the reaction time, all response times that were less than 0.100 s and more than 3.0 s were excluded as outliers. The duration of each trial was restricted to 800 ms with trail onset at the second flow in the pair, including a period after target off. For each condition, 30 different trials were included, a total of 60 trials.

Small-World Propensity
The phase synchronization across all possible pairs of electrodes, defined by the Phase Lag Index (PLI) [71,72] for each frequency band, measures the asymmetry of the distribution of the instantaneous phase differences using Hilbert transform. When the PLI is 0 then two signals have no phase difference. When a PLI has a value of 1, then the phase difference of those signals is different from 0 mod π. PLI is not sensitive to adulterated correlations due to adjacent source and volume conduction [71,72]. The networks are created from statistics over strengths of the connections (edges, links) between neighbored nodes. Several main metrics reflect the behavior at a global brain level of the network as segregation, integration, and hubness [73,74]. The ability of the network to process information within a region or a group of interconnected neighbored brain areas (so-called nodes) is described as segregation, while the network capacity to compound information between different regions of the brain (nodes) describes the network integration [75]. Graph measure, which characterizes brain network segregation, defined by a part of the adjacent neighbors of nodes, describes the clustering coefficient [76,77]. Graph measure, which characterizes the network integration, defined by a mean shortest length of the paths between all node pairs, describes the characteristic length of the path in the network [76,77]. The hubness includes measures of each node as strength of its connection to all other nodes, and betweenness centrality as the part of all shortest lengths of the paths cross the node in the network [73,74,78]. The part of all shortest lengths of the paths, containing a given edge, is the betweenness centrality of this link in the network. The small world is described from the ratio of the measures as the characteristic length of path and the clustering coefficient, as well as the global efficiency, quantified by the inversed mean length of the paths and described the information exchange across the network [74]. A new graph metric, called small-world propensity SWP, assesses the density variations of the network [79] and sensitivity to the strengths of functional connections between nodes. The weak and strong links have different contributions to the overall functioning of the network [80]. This method does not ignore the weak links because it does not apply thresholding techniques as in other approaches. These links can identify as potential pathological biomarkers [80]. The comparison of the characteristic path length and clustering coefficients of null models as random graph (L rand , C rand ) and regular lattice (L latt , C latt ) describes the smallworld structure of observed weighted networks (L obs , C obs ) by the SWP (denoted by φ). The nodes of these graphs have the same number and probability power distribution of degrees [79]. The deviations of the L obs and the C obs (∆L, ∆C) of the observed network from its null models quantifies φ: These models assume that adjacent nodes in the observed network are connected with higher strength and stronger edges than remote nodes. The observed edge weights are arranged in the lattice model of a weighted network. The highest weight is assigned to edges with the shortest Euclidean distance between nodes. The weights of edges are ranked by decreasing strengths. The randomly distributed connections with N highest weights across the edges and represented in a one-dimensional lattice with a unit distance. The next connections with N-1 highest weights across the edges are represented in a twodimensional lattice. In this way, all edges in the observed network are arranged in the lattice. The higher weights in the built lattice are assigned to distances that corresponded to the higher strength of near edges. The edges with the highest strength in the lattice network are located on the diagonal of the adjacency matrix. A high C latt and low L latt characterize the lattice network. The network rewires when the deviation ∆C is maximal. The random network has connections randomly assigned throughout the matrix and small shortest paths between them. The random network has small values of C rand and long lengths of L rand . When significant clustering between the nodes lacks locally that the random model is highly integrated and not segregated. These reference networks are important to calculate φ of an observed network. The observed networks can have values of L obs or C obs that exceed those of the lattice or random null models. If these measures are lower than 0 or higher than 1, then the φ sets to a range [0, 1]. The real word networks with high L obs and C obs (low deviations ∆L, ∆C) have φ ≈ 1. The values of φ close to 0 are associated with larger deviations ∆L and ∆C from the null models, a smaller small-world structure, and high measures of the small-world. The real power of φ quantifies the degree of small-world structures between the networks. Relatively large φ values of real networks indicate small-world properties. The real networks with high φ close to 1 are guided by big C obs and short L obs (low ∆C, low ∆L). A big C obs and moderate L obs (low ∆C, moderate ∆L), as well as modest C obs and short L obs (moderate ∆C, low ∆L), can drive the relative high φ. Smaller small-world structure with values of φ close to 0 is maintained by larger deviations ∆L and ∆C from the respective null models [79].
The adjacency matrices with 40 to 40 nodes of the weighted graph, built by PLI between all pair sensors, are estimated for each frequency band (δ ÷ γ). The SWP measures are estimated for controls and dyslexics, based on the Brain Connectivity Toolbox for MATLAB, at http://www.seas.upenn.edu/~dsb/, accessed on 1 January 2016 [79].

Statistical Analysis of Global SWP Measures
Group comparisons of the global φ, ∆L, ∆C measures are implemented by bootstrap nonparametric procedures with 1000 random permutations for each condition and frequency [81,82]. Independent permutation tests require corrections for multiple comparisons. The Bonferroni correction was applied to the significance level (p = α/3 = 0.017).

Statistical Analysis of Local SWP Measures
Local measures of the nodes in the network are strength and betweenness centrality (BC). The betweenness centrality of the nodes is defined through a conversion of the weights into distances in the adjacency matrix. A large number of shortest paths join in edges with high values of BC. The sum of the weights of links for each node defines its strength. The local characteristics of each node values are divided by their mean values between the nodes. Many shortest paths pass through nodes with high BC/strength, which have a substantial role in the information processing of the network [77]. A graph with maximum BC/strength is more integrated [73,78]. The most important nodes call hubs of the network. The local measures are estimated based on MATLAB's brain connectivity toolbox [74]. At the level of network nodes, the strength and BC of the nodes were evaluated by nonparametric permutation cluster-based statistics [81]. This analysis is performed for the hubs, defined by nodes with maximal strength/BC crossed the selective threshold criteria (one standard deviation over a mean group node's strength/BC). The significant clusters are identified by applying a critical value for the (max cluster) statistics. Throughout control of the false alarm rate with multiple comparison corrections, repeated clusters pass significantly the threshold criteria and defined an ordered sequence. The histograms of the nodes have indices corresponding to the sensors. The medians of their distributions are sensitive to the hemispheric differences. The control of the multiple selected thresholds requires Bonferroni correction (p = α/2 = 0.025). Non-parametric statistics are accomplished on MATLAB. The significant results are bold in the tables. The selection criteria are applied also for the links and edge BC, presented on the figures, drawn by BrainNet Viewer version 1.63 [83]. (See Appendix A).

Statistical Analysis of Behavior Parameters
The behavior parameters as a performance accuracy and reaction times during EEG sessions were compared between pre-training and post-training dyslexic groups and between neurotypical readers and dyslexics for each condition (low/high-speed contrasts) based on a nonparametric test (Kruskal-Wallis test [KW test]).

Behavior Measures
The first language of the participants was Bulgarian. The classification of hand preference [84] showed that all children had right-hand preferences. They were with normal or adjusted to normal vision. They scored ≥98 points in their nonverbal intelligence test [63]. Children who had difficulty reading, along with accuracy or speed in reading subtests of the DDE-2 battery and the "Reading Abilities" battery below the norm with a standard deviation of standardized data of normally reading children were included in the dyslexic group [85]. Children, participating in the study as controls, were recruited from the schools of the dyslexics. They were of the same age and socio-demographic background as the dyslexic group (Table A1). They did not have dyslexia and concomitant language disorders, according to the accuracy and speed of reading in DD2 tests (Table A1).

Impact on Motion Measures on Global SWP Measures
For the global SWP measures in the low-speed contrast of the radial flows, the significant differences were found between the controls and the pre-D in the θ ÷ γ1 frequency range, as well as between the pre-D and the post-D in β ÷ γ1. In the high-speed condition, the significant differences were found between the controls and the pre-D in the β2 frequency band as well as between the pre-D and the post-D in α, β, γ1. In both speed contrasts in the groups from θ to γ1 frequency ranges, there was a decrease in φ and ∆L, and an increase in ∆C with increasing frequency. The pre-D, compared to the controls, had statistically higher φ in α ÷ γ1 and ∆L in θ, β2 and γ1 bands for the low-speed contrast, while compared to the post-D-higher φ and ∆L in β1 ÷ γ1 (p < 0.01, χ 2 > 6.57; Table 2). For the high-speed contrast, the pre-D was with higher φ in β2 (p < 0.003, χ 2 > 8.65; Table 3) than the controls and with higher φ in α to γ1 and ∆L in α, β2 (p < 0.011, χ 2 > 6.43; Table 3) than the post-D. The pre-D had a statistically lower ∆C vs. controls in θ ÷ γ1 for low-speed (p < 0.008, χ 2 = 7.03; Table 2) and in β2 for the high-speed contrast ( Table 3: p = 0.002, χ 2 = 8.94), while vs. post-D-in β1 ÷ γ1 (p < 1. 2 × 10 −5 , χ 2 > 8.43; Table 2) and in α ÷ γ1 (p < 0.003, χ 2 > 8.46; Table 3). The post-D had a statistically higher ∆C and lower ∆L in β1-network compared to the controls for the low-speed contrast (∆C: p = 0.017, χ 2 = 5.68; ∆L: p = 0.006, χ 2 = 7.47; Table 2), while for the high-speed contrast-statistically lower φ and higher ∆C in α and β1 (p < 0.005, χ 2 > 7.75; Table 3). Table 2. Statistics of the global metrics (mean ± s.e.; φ; ∆C; ∆L) of the brain networks of the groups (Con, pre-D, post-D) during the slow-speed contrast of the radial flow for frequency bands: δ, θ, α, β1, β2, γ1, γ2 Hz.

Frequency/Metric
Con Pre-D Post-D
The hub distributions in the graphs of the γ2-frequency network (strength of nodes, Str) were significantly different between the controls and the pre-D (p = 0.0006, χ 2 = 11.73), as well as between pre-D and post-D (p = 6.12 × 10 −5 , χ 2 = 16.06). The difference in the hub distributions was due to the median of the distribution of the pre-D and controls was in the left hemisphere, while for the post-D-in the midline of the hemispheres. There was no difference in the distributions between the controls and post-D (p = 0.613, χ 2 = 0.25). For controls, the main hubs were located in left ATG (FT9), bilateral PRECG (Cz, C1-2), left PSTCG (C3) ( Figure 1D, 1st graph). For the pre-D, the hubs were in the left-hemispheric MFG (F3: BA8), IFG (F7), ATG (FT9), PSTCG (C3), and the right-hemispheric PRECG (Cz, C2), SPL (CP2). For the post-D, the hubs were distributed in the bilateral MFG (FC3), the bilateral PRECG (Cz, C1-2), and the left ATG (FT9) ( Figure 1D, 3rd graph).

Global Network Measures
The networks with a relatively high φ were guided by a low C obs and low L obs (big ∆C and short ∆L) at θ, α, and γ1-frequency, while the network with relatively moderate φ was driven by an equally contributing moderate C obs and L obs (moderate ∆C, moderate ∆L) in the β-network. The networks are rewired, when the lowest values of φ at β-frequency networks in the controls and post-D, than in the pre-D, represented larger deviations from the respective null models for C obs and L obs . It was most expressed in the post-D group. The controls and the post-D in the β-network had nodes with a moderate L obs and moderate locally significant C obs between the nodes in both speed contrasts. Therefore the network integration and segregation had an equal contribution for low/high-speed contrasts in these groups but with less segregation in the post-D than the controls due to lack locally of significant clustering between the nodes for β1-frequency range at low-speed condition, but with a more segregated network than before training. The groups' graphs exhibited different small-world properties. The networks in the controls had a similarly relatively low φ at α and β frequencies. The networks in the dyslexics before training had high φ at low-frequency networks, which gradually decreased through the middle frequencies, and passed into networks again with relatively high φ at γ1 frequencies. In the low-speed contrast, the lower values of φ of brain networks in the controls than other groups represented larger ∆C and ∆L from the respective null models for C obs and L obs for θ, α, and γ1-frequencies, in which the networks are rewired. While at β (both speed contrasts) and γ1-frequency range, the post-D expressed lower φ comparing with other groups, where its network was rewired. The rewiring of the neural network suggests that the low-frequency transitions in theta/beta frequencies reset the neural activity occurring at γ frequencies as for selective attention [89], while the rewire at the high-frequency transitions in β/γ1 frequencies might be a more general process across other modalities. The visual stimuli might expose changes in visuospatial attention on a neural level of visual areas, which sampling rate for visual search is in the range of low γ frequencies and not the much slower δ/θ rate that shows no deficit [13,58,85]. The controls and the post-D in γ1-frequency range had moderately integrated and segregated networks for a low-speed condition and more segregated in both groups than the pre-D. In γ1-frequency band, the post-D compared to pre-D network structure with increasingly φ became less integrated and more segregated, driven by a large ∆C and low ∆L for the low-speed discrimination, and with the significantly higher change in the ∆C for the high-speed contrast.
Only, the visual processing speed, i.e., the component of visual attention capacity, affects the reading speed [58,90], is determined by the γ-frequency oscillations, whose range is the essential rate-limiting step in reading [13]. The visual attention span influences reading performance [91]. Generally, the sampling rate, used for reading, is selected for visual search and this range is itself under certain constraints in the processes of information integration and segregation. The main deficiencies in dyslexia may be impaired γ1 frequency sampling, affecting visual motion processing, (hence reading, [58]), and/or deceleration at this rate. The change in the frequency synchronized oscillations may affect the modulation efficiency of the motion-sensitive areas by the top-down feedback. Facilitations of sensory signals, arriving in sensory-sensitive areas, at which frequency alterations would lead to a mismatch with the resonant frequencies in the primary visual area. These frequency changes might lead to poorer neuronal oscillations in dyslexics at the speed-motion processing. There may also be some slowing down of the sampling rate, which was better after training. The consequences would be a slowdown by reducing speed due to slow sampling range and faster by overloading the working memory capacity due to fast frequency sampling range and time, needed for high-speed processing. If the attention spotlight spans more globally the flow at a time in each γ-cycle, the speed processing may be slower. The sensory inputs get parsed at a rate of 4 Hz [92], which is in the theta frequency range that has been involved in the network differences between dyslexics and controls at the slow-speed flow discrimination. Essential for decoding of information processing in the flow parsing was the identification of speeds, which for most readers occurred at β2-γ1 (20-30 Hz, 30-48 Hz) rates. This process can determine the frequency of saccades. The decreasing attention at the preferred γ frequency will limit in time of eye fixation when the speeds that can be sequentially identified can trigger the efferent oculomotor signals at the θ frequency. The critical parsing for speed recognition may be limited to the γ1 range. Low-frequency oscillations have been reported in brain areas related to sustained visual attention [93] and modulation of visual awareness in different time scales. Neural oscillations, ranging from the δ to α frequency range at visual awareness, are linked to cognitive processes, [94]. Hence, the most optimal rates of perceptual and cognitive systems in the child depend on the temporal characteristics related to speed identification but do not necessarily determine the processing of speed motion in the visual system.

Local Network Measures
The neural network covered from the occipital, temporal, and parietal to the frontal cortex, spanning regions in the lateral occipital (LOR), parieto-occipital (V6), superior temporal (the middle temporal cortex V5/MT+), IPS, lateral part of the intraparietal LIP, V3A/V7, and the superior frontal (SFS) sulci in both brain hemispheres. The low-speed discrimination (θ Str,BC ) resulted in significant nodes at the cuneus bilaterally at the controls and with a focus on the left cuneus in the post-D, located slightly dorsal to the focus in the primary visual cortex, as well as at the supplementary motor cortex (SMA). Also, the low-speed discrimination yielded significant nodes in the left medial frontal cortex and the right visual area V5/MT+ and MST+ of the controls, as well as the left occipitotemporal cortex in both control and post-D groups. An extensive visual network included early visual areas, MT/V5+, V3A, sensory-motor cortices, as well as inferior frontal regions (IFG) at the left hemisphere for the controls and the right one for the post-D. In the θ-frequency network, the viewing of uniformly low-speed radial textured pattern to almost static flow cue identified nodes at areas MT/V5+, V3A, bilateral cuneus, several regions along with the dorsal extent of the IPS and bilateral nodes of two parietal motion-responsive regions for the controls and post-D, which were significant only in the right hemisphere for the trained dyslexics. The low-speed stimuli recruit θ frequency modulation at occipital and motion-responsive regions MT/V5+, MT/MST, and less at the posterior parietal and occipitotemporal regions of pre-D (θ BC ). Increasingly nodes in post-D (θ, β2, γ2 Str ) at the high-speed discrimination appeared in the frontal cortex than other groups. One site was located in the medial frontal gyrus, one in the middle frontal gyrus. The region along the right dorsal IPS exhibited significant nodes in post-D than pre-D (β2, γ2 Str , high-speed contrast).
At β1 frequency range, the nodes in areas, activated by attention to speed as a right dorsal V3, appeared within the more difficult condition (at low-speed contrast) before training and in the left hemisphere after training. Regions that hubs were observed at the more difficult contrast were localized in the left superior frontal and IFG, the precuneus, left inferior parietal lobule, left post-central, right superior temporal gyri, right temporal, medial temporal lobes bilaterally for the controls, in the controversial hemisphere at the frontal areas for post-D (θ Str ). For low-speed conditions (θ BC ), the nodes indicated that the effects of attention to speed were in V3v/V4v, V3d, and V3A/V7 for the controls and post-D, where the V4 was not active in either hemisphere in the pre-D at any frequency range. In addition to V3 bilaterally, right V3A/V7, and left V3v/V4v, the hub was localized adjacent to the left fusiform gyrus for the controls and the post-D (θ BC ), in the right frontal cortex as well as in the left post-central gyrus for the post-D (θ Str,BC ), was not present in the pre-D. The MT/V5+ was more active during the slow-speed contrast than in the high-speed for the controls and post-D, and was not present in the pre-D. Only the precuneus (7P) was active for the high-speed contrast in the dyslexics before and after training. There were more hubs at V3A in high-speed contrast than in slow-speed for controls and post-D for all frequency ranges, while it was present in the pre-D only at the low-speed discrimination (β1). Increasing the speed contrast moderately affected V3d, but engaged several non-visual, mostly frontal regions for the controls (θ, low-speed; γ2 high-speed) and the post-D (β2, γ2, high-speed contrast). The oscillation activity of the right dorsolateral and ventrolateral prefrontal cortices increased at the high-speed contrast in both dyslexic groups. The low-speed contrast increased the frequency oscillations of the right middle frontal focus for the post-D and left middle frontal focus for the controls.
Decreased accuracy in the more difficult contrast caused increased node' number in frontal regions, including a right IFG, a right prefrontal cortices in the post-D due to an increase in the executive activity or attention [95]. With increasing task difficulty, deactivations were observed mostly in left-sided parietal areas in pre-D but increased in the right hemisphere (θ Str,BC ). These regions did not show a trend of deactivation during highspeed contrast for pre-D compared to the low-speed contrast. The increases in difficulty enhanced the attention effect in the dorsal V3, which is important for all groups. However, the stronger responses in the controls and the post-D could be due to V4 involvement during fine discrimination compared to coarse speed discrimination [96]. Together with the selective response in V5/MT+ (θ-frequency range) for the controls and post-D to the lowspeed motion contrast, nodes were observed in the left-side superior and lateral parietal cortices, SMA, and the lateral occipital region as well for the pre-D and post-D groups (β1). The area POs/V6 responded more to complex visual stimulation in the high-speed contrast for the post-D at β2 and γ2-frequencies.
The motion regions in the lateral occipital sulcus (LOs), V3A/V7, MT, POs/V6, and regions in the LIP [97], at the end of the posterior part of the Sylvian fissure, superior frontal sulcus, involve in the flow parsing mechanism due to extracting information for object-motion from motion on the retina by taking out the optic flow components [43]. The images of an object move across the retina during the head movement in synchrony with the head [98]. The children perceived the optic flow cue, almost like a fixed on the screen, as static and the high-speed contrast flow as shifting out the screen. The perception of flow-motion is not simply the result of the motion of the image on the retina or the screen but must be comprehended information for the subject motion. An area, adjacent to the anterior part of the precuneus and the portion of the SPL (IPS/7P, [99]) was involved in the right hemisphere for the controls at the high-speed contrast (β2 Str ) and the low-speed contrast for the pre-D (β1 Str ), while only the precuneus was involved for the dyslexic groups at the high-speed contrast (θ Str ). The cortex between areas V3, the adjacent to the anterior part of the precuneus and the posterior part of the SPL, occupying the anterior bank of POs, with the ventral region on borderline of an area with an occipital pattern and a dorsal part on borderline of an area with a parietal pattern, corresponding to V6Av and V6Ad [100]. The motion area POs/V6 responds to a unidirectional movement [50], coding the motion together with MT, and is sensitive to the flow field [50,101]. It is sensitive to optic flow patterns combined with different, but near-field stimuli cue [102], and only this area among the other motion areas prefer complex visual motion [43]. The area POs/V6 of the post-D (β2, γ2) responded more to the high-speed than to the low-speed flow contrast (β1). At the low-speed (θ Str,BC ) and high-speed contrasts (γ2 Str ), only the controls showed hubs in the left hemisphere at the motor area, the overlapped part of the superior frontal gyrus which lies inferior to the motion-sensitive pre-supplementary motor area [43].
The visual flow motion cues stimulated the vestibular cortex, distributed across multiple anatomical structures across the parietal cortex with a boundary between the supramarginal and angular gyri (SMG, AG), strongly connected with the temporal-parietal junction involved the SMG and the STS [103]. Also, along another area, corresponding of the lateral end of the central sulcus and together with the superior temporal cortex was stimulated by visual low-speed flow cue in the right hemisphere for the controls and post-D (θ Str , β1 Str ) and showed strong connections in both hemispheres to the Heschl's gyrus, precuneus, IPS, parietal cortex, anterior temporal cortex (ATL), and the IFG. These nodes were located in the left hemisphere for pre-training children with dyslexia (θ Str,BC , low-speed flow). The high-speed flow involved hubs in STS and Heschl's gyrus at the left hemisphere of the control at γ2, the post-D at θ and β2-frequencies, and the right hemisphere of the pre-D at the β2.
The motion-sensitive area, located on the LOs is part of the kinetic occipital region [104], overlaps the dorsal area V3 [105]. This area responded significantly to the low-speed flow than to the high-speed flow in both controls and post-D (θ). The motionsensitive MT+ complex (MT and MST areas) between the inferior temporal and the middle temporal sulci [43] is involved in ego-motion perception [47]. Areas V3A/V7 (low-speed: pre-D, β1 right , post-D, β1 left ; high-speed: post-D, β2 right , and controls, γ2 right hemisphere ) in the ventral part of the posterior IPS likely correspond to the dorsal V3A [43], and posteriorly/laterally to the POs/V6, respond to the flow field stimulation [47,106,107], other type global motions and reconstruction of form from motion [108].
The motion-sensitive region VIP, located along the horizontal segment of the IPS to the ventral part of the IPS and anteriorly to V3A [109] responded more to the low-speed contrast for the controls and post-D (θ left for both groups; β1 left for post-D, β1 right for controls) than to the high-speed contrast (θ right for controls, and γ2 right for post-D). While for the pre-D, VIP responded only to the low-speed contrast (β1-frequency in the right hemisphere). The area LIP (BA7/5) in the dorsal part of the IPS connects the horizontal segment and posterior part of IPS, anteriorly to V3A. For the control and pre-D groups, the LIP responded more to the low-speed contrast (pre-D: right-side θ, β1, γ2; controls: θ, β1) than to the high-speed (pre-D: β2 both-sides , γ2 right ; controls: β2 right ), while for the post-D-more to the high-speed (θ left , γ2 right ) than to the low-speed contrast (β1 left ). The region in the superior frontal sulcus (SFS), partially overlaps the superior part of the frontal eye fields (FEF), is responded more to the high-speed than to low-speed contrast for the controls and post-D in θ Str , while for the pre-D was involved in both speed-contrasts in the higher frequency range (γ2, low-speed; β2, high-speed). There were nodes adjacent to regions V6, superior parietal lobule (SPL), precuneus, motor area, regions in LOs, LIP, SFS, VIP, V3A/V7, and MT+ that were selected at least one of the speed-motion conditions. The other nodes included areas that were found in specific frequency networks V6+, MT/MST+, SPL, precuneus. Some of these areas may reveal object-motion (MT) from self-induced motion (SFS) during the optical flow cue or both self-motion and object-motion (V6, VIP, LIP, MST+, V3A). These areas were induced by the flow stimulus [43], whereas some of them perceived complex visual stimulation (MST+, V3A).
The motor area is responsible for the head and body movements in space [110], for the self-motion perception, the integration of motion information from visual and vestibular senses [110], and visuospatial attention [111]. The region LOR in LOs, sensitive to a motion of radially moving stimuli [50], is part of the kinetic occipital region [104]. The nodes were observed at this region of the controls and post-D, which discriminated the difference between the two slow-speed motions of the image on the screen, probably due to the selfmotion preference of this region as well. The precuneus frequently associates the motion network [112] to egomotion [51], responding to self-motion more than object-motion [43]. The area, adjacent to the anterior precuneus and the portion of the SPL, integrates visual self-motion signals with locomotion movements [43]. The activity of LIP and SFS/FEF, part of the dorsal attention network, is mainly eye-movement/attention-related [97,109,113,114], and differently, modulate at various motion conditions [115]. The motion-sensitive areas in lateral and medial temporoparietal regions, responding to self-motion (LOR), objectmotion (MT), and both motions (V6+, V3A, and VIP) are joined in the network of the flow-parsing mechanism, distinguishing the different optic flow's components [116]. This network provides an internal visual field presentation as interprets correctly the motion and provides a stable perception of the sensory changes induced by the eye and selfmovements [52]. The flow parsing-related regions integrated the early visual areas and higher-order regions with different functional properties in the visual motion processing, ego-motion processing with relation to object-motion [44,45]. Independently of actual eye movements [117], the parietal eye fields (PEFs) are involved in the shift of spatial attention even with eye movement constraints [118], as these movements cannot completely be ruled out in motion conditions. The modulations of early visual areas mediate by synchronized neuronal top-down oscillations [118,119] from the posterior parietal cortex (PPC) with a frequency of 25-45 Hz [120] and those from the prefrontal cortex to the PPC with a frequency range of 22-34 Hz [121]. Top-down oscillations from the PPC to MT and further to V1 [13], which participate in serial visual search, can also be used for speed discrimination as well as for reading [58]. In the low γ range, discrete information from a single object can be identified and processed concurrently in the ventral stream for perceptually binding with a flow cue. Spatial attention in a serial search, directed by FEF with the frontoparietal synchrony, serially activates LIP during object locations and produces each oscillatory γ cycle in LIP, emphasizing one of the locations in the visual field. The shifts of the covert attention were observed through the β2 oscillations in the FEF-PEF at the dyslexics before training (high-speed condition). After training, the frontoparietal network is trained to make a similar serial but spatially sequential switching of top-down focal attention through β1-network (low-speed condition). For the low-speed discrimination, the sampling bandwidth is limited to the frequencies in the range of β1, thus, the parsing flow at the lower frequency range prevents from overloaded the subsequent cognitive processing at the post-D. For top-down modulation, frequencies in the β2-γ1 range  are used at the early visual areas and the parietal cortex [120]. It is assumed that flow parsing and visual search depend on oscillations that mediate significant cortical interactions and are locked into a narrow frequency range of the β2 range of the neural synchrony that carries out these interactions. The physiological reasons due to these frequency oscillations are in this relatively narrow range [122] are to facilitate the synchrony within the areas and between the areas [123,124]. In high-speed discrimination, the neuronal oscillations for top-down processing are in the β2-γ2 range, which resonates best with all neuronal circuits that have fast integration times (15, 50 ms). While synchrony within the visual areas may be driven by higher γ frequencies [125], the synchronization between the LIP and the visual areas feedback is slower in the β1-frequency range at the children with dyslexia (low-speed condition). At the controls (high-speed contrast), but not in the pre-D, the feedback from areas MT/MST to the visual areas is mediated by the top-down γ2 frequency network, in which the neural circuitries with resonance properties are embedded. The basic deficit in dyslexics may be either impairment of the gamma sampling or its amplitude, affecting the visual search of flow parsing. A change in amplitude/frequency of the high-frequency oscillations could affect the modulation efficiency of the primary visual area by the top-down feedback. These changes revealed disability in the γ frequencies in the visual areas of dyslexics at the high-speed discrimination.

Local FEF-PEF Network Measures
The stimulus direction triggered the reflexive saccades and elicited activation of the FEF (BA6/8), supplementary eye field SEF (dorsal medial frontal lobe, rostral supplementary motor area, the premotor cortex, BA6), PEF (BA 39/40), and additionally the dorsolateral prefrontal cortex (DLPFC; BA9 and BA46) by triggered voluntary saccades [126,127]. The FEF, along with the posterior temporoparietal areas, controls pursuit eye movements (PEMs) [128]. The SEF involves in motor programs immediately before the execution of the motor sequence, comprised several successive saccades combined with a body movement. While a more anterior region of SEF is included during the visual sequence of stimuli [126]. The DLPFC is involved in the inhibition of saccades, decisional processes, and short-term spatial memory [126]. DLPFC controls memory-guided saccades when spatial memory is involved during the delay period [126,129].
Nodes at the left FEF and PEF were found in the control (θ, both contrasts) and post-D groups (β1, low-speed; γ2, high-speed condition). However, there were no nodes in the PEF of the pre-D group in contrast with compensatory nodes in FEFs (θ, γ2, lowspeed contrast), SEF, and concomitant relative hyperactivity in the dorsolateral prefrontal cortex (θ, high-speed contrast). An imbalance between FEF and PEF (a node only in the PEF) was also observed in the β1-frequency network of the pre-D for low-speed discrimination, which reflected reorganization of functional connectivity. The relation of dopaminergic network reorganization with functional plasticity within the oculomotor network takes advantage of the well-known circuitry in the FEFs (BA6/8) [126] and the PEFs (in BA39/40). The children with dyslexia have shown shifts of FEF vs. PEF nodes in β1-frequency network or imbalance of their node's distribution in the oculomotor system. This coupled reorganization at a functional level could be related to the basal ganglia with privileged input to FEFs, facilitating or inhibiting the saccade's executions [129]. The saccades and pursuit eye movements elucidate complex neuropsychological processes related to the processes of attention, spatial memory, motivation, and decision. The dorsolateral prefrontal cortex controls decisional processes [126] for the children with dyslexia at the high-speed discrimination (θ for pre-D; β2 for post-D), governed oculomotor behavior, guided the pursuit eye's movement control, and unwanted reflexive saccade inhibition. The role of PEF in visual-spatial integration and attention is guided only by β1-frequency networks for the dyslexics before and after training at the low-speed discrimination and for the post-D at high-speed condition by γ-frequencies. The FEF also controls optokinetic nystagmus [130]. The involvement of FEF in the pursuit eye's movement may be accompanied by the deactivation of areas responsible for the vestibular control [131]. At the brain level, the interactions between the visual and vestibular systems that support the self-motion perception may be reciprocally inhibited. Hyper-activation of FEF was observed for the pre-D (high-speed condition). The control of DLPFC for inhibiting improperly directed saccades to the stimuli probably has not been very effective for a long time at [126] the pre-D during the high-speed discrimination. The activation in the FEF but not in the PEF, confirm that intentional saccades have an early preparation but not the latter only for the pre-training dyslexics (θ, γ2, low-speed; θ, β2, γ2, high-speed contrast). The DLPFC may inhibit the reflexive saccades without involving other cortical areas [132] at the pre-D (high-speed contrast) due to direct involvement of the superior colliculus via a prefrontal-collicular tract [133].
The activation of the PEF is related to visual-spatial integration of the information [134] at the anterior portion of the IPS (limited medially by the SMG, BA40), involved more in eyehand coordination [135][136][137], and at the posterior part of the SPL involved in attentional processes [136][137][138][139]. The nodes over these areas suggest better eye-hand coordination and attention for the controls and post-training dyslexics. Visual information from the occipital lobe passes over the parietal lobe through the attentional areas in the posterior SPL, the PEF, and the IPL (SMG or AG), which have specific roles in attentional control [126]. The SMG (BA40) is involved during saccades [113] and the AG (BA39)-during reflexive saccades [140]. The parietal-FEF projections are mainly involved in visual fixation [141]. The nodes over the PEF (or an adjacent area), which controlled visuospatial integration were more expressed in the post-D and controls. Therefore, at a delayed response, the transfer of visual information from the PEF to FEF is to accomplish the active fixations at the controls and from the intraparietal areas to the DLPFC is to memorize the short-term spatial events at the post-D. The DLPFC governs decisional processes of oculomotor behavior. It is related to inhibition of reflexive saccades controlled by the PEF or facilitating the triggering of anticipatory saccades controlled by the FEF [126]. There were no nodes at DLPFC for the control group. Probably, the superior colliculus directly exerts the inhibition of reflexive saccades [126]. The pursuit eye movements are controlled by the posterior hemispheric areas, closed to the AG at the temporal-parietal-occipital junction, but also by the FEF [126]. The generators of pursuit eye movements were expressed for the controls and post-training dyslexics but less expressed for the pre-D group.

Constraints
The juxtaposing of the brain network to the lattice and random models is of particular importance for statistical comparisons of the brain networks. For the brain networks, the validation of some significantly differing measures depends mainly on the metrics of the null models. The metrics of the models are related to the tested hypothesis. The distribution of the degree/power of the real network is widely used in the null models. In different categories (edge level and spectral graph, nodal level, and global level), graph measures of brain networks are statistically compared between healthy and patient groups. The presented metrics, in this study, described integration/segregation and hubness of brain networks. However, in neuroscience, other network metrics could reveal no obvious network differences. This is often an empirical choice. The choice of these measures should be guided by the pathophysiology of the main question in the neuroscience study. The provocation is to apply many metrics that can depict the differences in the graph without missing any information. Some graphical algorithms useful for detecting uncaptured metrics are still limited to graph analysis called non-directed. Broader algorithms with directed/causal functional networks need to be developed.

Conclusions
Medial superior temporal area (MST), considered part of the parietal stream, encoded visual-spatial orientation with a direct projection to VIP, area on the lateral part of the IPS. Area VIP was involved in directional and speed selectivity of expansion optic flow (controls, θ low-speed flows). The inferior parietal lobule is involved to distinguish radial optic flow direction (expansion from the center to periphery), which was not existing in either MST or SPL (BA7). Like MST, IPL responded to the speed discrimination. The optic flow selectivity and speed dependence interact at a slow-speed contrast of at expanded optic flows. Unlike MST, the superior temporal cortex STC prefers radial expansion, but not the direction of motion. STC received projections from area MST and SPL. The dorso-caudal part of the SPL (BA5/7), as a subdivision of the somatosensory cortex, sends a direct input to the premotor cortex. The SPL is associated with visual stimuli and participates in the integration of visual-motor signals. Information about the heading movement can be provided from MST and VIP, sensitive to the focus of expansion with respect to the fovea [142]. The motor cortex is one of the optic flow areas and showed a bias for expansion flow for all groups and contrasts. The parietal-frontal circuit is involved in specific sensorimotor transformations. Various other signals are incorporated to successively integrate somatosensory, visual, proprioceptive, and motor eye position information to produce a final motor output. The MT/V5 analyzes the speed and motion direction in the central visual field for the controls and post-D group at low-speed-contrast. While for the high-speed contrast, POs/V6 finds out self-motion across the whole visual field. The periphery of the flow is more emphasized in POs/V6 at low-speed-contrast in β1-network of the pre-D group but not at the high-speed contrast. This supports the hypothesis for the disability of POs/V6 to view the whole visual field. Therefore, the dorsal stream comprises upwards the parietal lobe over the hierarchies from V1 to POs/V6 along with the V1, V3A, MT+, SPL/7A, FEF further down in lateral IPS, does not include POs/V6, MT/MST, and the prefrontal language brain areas (Broca area) of pre-training dyslexics at the high-speed contrast and V5/MT+ at both conditions. The MT+ also includes the medial temporal gyrus (BA21), associated with accessing word meaning while reading. The disability of occipitotemporal gyrus, adjacent to posterior fusiform area and area V4 of the pre-D was also found for the low-speed contrast in the ventral stream at the sequence VI, V2, V3, V4, inferior temporal cortex. The ventral stream starts with simpler features posteriorly in the posterior inferior temporal cortex (including fusiform cortex), sensitive to orientation-selective within a form, and motion direction, object recognition, visual attention, and visual language perception. Then, the ventral stream includes areas with the increased complexity of processing at the anterior temporal cortex to carry out flow recognition, and asymmetrically, tending to the left hemisphere for the other control and post-training groups. Disability in the integration of both dorsal and ventral stream information into motion processes was found at the areas, limited medially by the SMG (BA40), within the anterior part of the IPS, these areas transfer the information between the perceptive and motor systems to control the arm and eye movements in pre-D at the high-speed flow.
A deficit in the orienting of spatial attention at developmental dyslexia is involved in visual hemineglect due to a disorder of the right posterior temporoparietal cortex, usually in the superior temporal region [143] or in the temporoparietal junction (IPL; [144]). Along with deficits in parietal and prefrontal areas, involved in rapid auditory and phonological processing, impairments in the temporoparietal and dorsolateral prefrontal areas are included, engaged in directing and sustaining visual attention. The disruptions of pathways connecting different brain structures as well as deficits in motor and oculomotor coordination coexist with the dysfunctions in the posterior temporoparietal and the prefrontal cortex. That supports the suggestion of developmental dyslexia as a deficit of an extended cortical network [58], which dysfunctions were compensated in the dyslexics after visual training [145][146][147]. Data are expressed as the mean ± SD. Forty-six children: 25 children with dyslexia (10 boys and 15 girls, age 8.76 ± 0.53 years) and 21 normal children (11 boys and 10 girls, age 8.8 ± 0.36 years) from a second grade of four primary schools located in the urban community of middle-level socio-economic status in Sofia, Bulgaria. The study was conducted in the schools. The children had a normal or corrected-to-normal vision after an examination by an ophthalmologist. All participants in the study spoke Bulgarian as their first language and were right-handed. Table A2. Statistics of local graph SWP metrics (strength: Str; betweenness centrality: BC) of functional brain networks of control and dyslexics groups during slow speed of the radial optic flow presentation for frequency: δ, θ, α, β1, β, γ1, γ2 Hz.