Small-world Network Organization Research Articles

Fractured columnar small-world functional network organization in volumes of L2/3 of mouse auditory cortex.

The sensory cortices of the brain exhibit large-scale functional topographic organization, such as the tonotopic organization of the primary auditory cortex (A1) according to sound frequency. However, at the level of individual neurons, layer 2/3 (L2/3) A1 appears functionally heterogeneous. To identify if there exists a higher-order functional organization of meso-scale neuronal networks within L2/3 that bridges order and disorder, we used in vivo two-photon calcium imaging of pyramidal neurons to identify networks in three-dimensional volumes of L2/3 A1 in awake mice. Using tonal stimuli, we found diverse receptive fields with measurable colocalization of similarly tuned neurons across depth but less so across L2/3 sublayers. These results indicate a fractured microcolumnar organization with a column radius of ∼50 µm, with a more random organization of the receptive field over larger radii. We further characterized the functional networks formed within L2/3 by analyzing the spatial distribution of signal correlations (SCs). Networks show evidence of Rentian scaling in physical space, suggesting effective spatial embedding of subnetworks. Indeed, functional networks have characteristics of small-world topology, implying that there are clusters of functionally similar neurons with sparse connections between differently tuned neurons. These results indicate that underlying the regularity of the tonotopic map on large scales in L2/3 is significant tuning diversity arranged in a hybrid organization with microcolumnar structures and efficient network topologies.

Disrupted topological organization of white matter structural networks in high myopia patients revealed by diffusion kurtosis imaging and tractography.

High myopia (HM) is a public health issue that can lead to severe visual impairment. Previous studies have exhibited widespread white matter (WM) integrity damage in HM patients. However, how these WM damages are topologically related, and the network-level structural disruptions underlying HM has not been fully defined. We aimed to assess the alterations of brain WM structural networks in HM patients using diffusion kurtosis imaging (DKI) and tractography in the present study. Individual whole-brain and ROI-level WM networks were constructed using DKI tractography in 30 HM patients and 33 healthy controls. Graph theory analysis was then applied to explore the altered global and regional network topological properties. Pearson correlations between regional properties and disease duration in the HM group were also assessed. For global topology, although both groups showed a small-world network organization, HM patients exhibited significant decreased local efficiency and clustering coefficient compared with controls. For regional topology, HM patients and controls showed highly similar hub distributions, except for three additional hub regions in HM patients including left insula, anterior cingulate and paracingulate gyri (ACG), and median cingulate and paracingulate gyri (DCG). In addition, HM patients showed significantly altered nodal betweenness centrality (BC) mainly in the bilateral inferior occipital gyrus (IOG), left superior occipital gyrus (SOG), caudate nucleus, rolandic operculum and right putamen, pallidum, and gyrus rectus compared with controls. Intriguingly, the nodal BC of left IOG was negatively correlated with disease duration in HM patients. Our findings suggest that HM exhibited alterations in WM structural networks as indicated by decreased local specialization. This study may advance the current understanding of the pathophysiological mechanisms underlying HM.

Alterations of neural network organization during REM sleep in women: implication for sex differences in vulnerability to mood disorders

BackgroundSleep plays an important role in vulnerability to mood disorders. However, despite the existence of sex differences in vulnerability to mood disorders, no study has yet investigated the sex effect on sleep network organization and its potential involvement in vulnerability to mood disorders. The aim of our study was to empirically investigate the sex effect on network organization during REM and slow-wave sleep using the effective connectivity measured by Granger causality.MethodsPolysomnographic data from 44 healthy individuals (28 men and 16 women) recruited prospectively were analysed. To obtain the 19 × 19 connectivity matrix of all possible pairwise combinations of electrodes by Granger causality method from our EEG data, we used the Toolbox MVGC multivariate Granger causality. The computation of the network measures was realized by importing these connectivity matrices into EEGNET Toolbox.ResultsIn men and women, all small-world coefficients obtained are compatible with a small-world network organization during REM and slow-wave sleep. However, compared to men, women present greater small-world coefficients during REM sleep as well as for all EEG bands during this sleep stage, which indicates the presence of a small-world network organization less marked during REM sleep as well as for all EEG bands during this sleep stage in women. In addition, in women, these small-world coefficients during REM sleep as well as for all EEG bands during this sleep stage are positively correlated with the presence of subclinical symptoms of depression.ConclusionsThus, the highlighting of these sex differences in network organization during REM sleep indicates the presence of differences in the global and local processing of information during sleep between women and men. In addition, this small-world network organization less marked during REM sleep appears to be a marker of vulnerability to mood disorders specific to women, which opens up new perspectives in understanding sex differences in the occurrence of mood disorders.

The sleep network organization during slow-wave sleep is more stable with age and has small-world characteristics more marked than during REM sleep in healthy men

Sleep plays an important role in cognitive functioning. However, few studies have investigated the sleep network organization. The aim of our study was to empirically investigate the presence and the stability with age of a small-world network organization during REM and slow-wave sleep using the effective connectivity measured by the Granger causality. Polysomnographic data from 30 healthy men recruited prospectively were analysed. To obtain the 19 × 19 connectivity matrix of all possible pairwise combinations of electrodes by the Granger causality method from our EEG data, we used the Toolbox MVGC multivariate Granger causality. The computation of the network measures was realised by importing these connectivity matrices into the EEGNET Toolbox. Even if all small-world coefficients obtained are compatible with a small-world network organization during REM and slow-wave sleep, slow-wave sleep seems to have a small-world network organization more marked than REM sleep. Moreover, the sleep network organization is affected greater by age during REM sleep than during slow-wave sleep. In healthy individuals, the highlighting of a sleep network organization during slow-wave sleep more stable with age and with small-world characteristics more marked than during REM sleep may help to better understand the global and local processing of information during sleep.

Human Fetal Brain Connectome: Structural Network Development from Middle Fetal Stage to Birth.

Complicated molecular and cellular processes take place in a spatiotemporally heterogeneous and precisely regulated pattern in the human fetal brain, yielding not only dramatic morphological and microstructural changes, but also macroscale connectomic transitions. As the underlying substrate of the fetal brain structural network, both dynamic neuronal migration pathways and rapid developing fetal white matter (WM) fibers could fundamentally reshape early fetal brain connectome. Quantifying structural connectome development can not only shed light on the brain reconfiguration in this critical yet rarely studied developmental period, but also reveal alterations of the connectome under neuropathological conditions. However, transition of the structural connectome from the mid-fetal stage to birth is not yet known. The contribution of different types of neural fibers to the structural network in the mid-fetal brain is not known, either. In this study, diffusion tensor magnetic resonance imaging (DT-MRI or DTI) of 10 fetal brain specimens at the age of 20 postmenstrual weeks (PMW), 12 in vivo brains at 35 PMW, and 12 in vivo brains at term (40 PMW) were acquired. The structural connectome of each brain was established with evenly parcellated cortical regions as network nodes and traced fiber pathways based on DTI tractography as network edges. Two groups of fibers were categorized based on the fiber terminal locations in the cerebral wall in the 20 PMW fetal brains. We found that fetal brain networks become stronger and more efficient during 20–40 PMW. Furthermore, network strength and global efficiency increase more rapidly during 20–35 PMW than during 35–40 PMW. Visualization of the whole brain fiber distribution by the lengths suggested that the network reconfiguration in this developmental period could be associated with a significant increase of major long association WM fibers. In addition, non-WM neural fibers could be a major contributor to the structural network configuration at 20 PMW and small-world network organization could exist as early as 20 PMW. These findings offer a preliminary record of the fetal brain structural connectome maturation from the middle fetal stage to birth and reveal the critical role of non-WM neural fibers in structural network configuration in the middle fetal stage.

Altered Rich-Club and Frequency-Dependent Subnetwork Organization in Mild Traumatic Brain Injury: A MEG Resting-State Study.

Functional brain connectivity networks exhibit “small-world” characteristics and some of these networks follow a “rich-club” organization, whereby a few nodes of high connectivity (hubs) tend to connect more densely among themselves than to nodes of lower connectivity. The Current study followed an “attack strategy” to compare the rich-club and small-world network organization models using Magnetoencephalographic (MEG) recordings from mild traumatic brain injury (mTBI) patients and neurologically healthy controls to identify the topology that describes the underlying intrinsic brain network organization. We hypothesized that the reduction in global efficiency caused by an attack targeting a model's hubs would reveal the “true” underlying topological organization. Connectivity networks were estimated using mutual information as the basis for cross-frequency coupling. Our results revealed a prominent rich-club network organization for both groups. In particular, mTBI patients demonstrated hyper-synchronization among rich-club hubs compared to controls in the δ band and the δ-γ1, θ-γ1, and β-γ2 frequency pairs. Moreover, rich-club hubs in mTBI patients were overrepresented in right frontal brain areas, from θ to γ1 frequencies, and underrepresented in left occipital regions in the δ-β, δ-γ1, θ-β, and β-γ2 frequency pairs. These findings indicate that the rich-club organization of resting-state MEG, considering its role in information integration and its vulnerability to various disorders like mTBI, may have a significant predictive value in the development of reliable biomarkers to help the validation of the recovery from mTBI. Furthermore, the proposed approach might be used as a validation tool to assess patient recovery.

Disrupted brain connectivity networks in acute ischemic stroke patients.

Neuroimaging studies have shown that local brain lesions could result in abnormal information transfer far from the lesion site in acute ischemic stroke (AIS) patients; yet, little is known about alternations of the topological organization of whole-brain networks in AIS. By using resting state functional magnetic resonance imaging (MRI) and graph theory analysis, we systematically investigated the topological properties of the functional brain networks of 28 healthy controls (HC, age: 56.9 ± 0.45years) and 29 AIS (age: 57.6 ± 0.21years) with proximal anterior circulation occlusion within 12h of symptom onset. In our results, both the AIS and HC groups exhibited small-world network organization, suggesting a functional balance between local specialization and global integration. However, compared with the HC, the AIS patients had a lower shortest path length and higher global efficiency, indicating a tendency of randomization in patients' functional brain networks. The AIS patients had an increased nodal degree in the precuneus (PCUN), middle frontal gyrus (MFG), medial part of the superior frontal gyrus (SFGmed), orbital part of the middle frontal gyrus, and the opercular part of the inferior frontal gyrus, and increased nodal efficiency in the PUCN, MFG, SFGmed, and the angular gyrus. The decreased nodal degree in AIS was found in the heschl gyrus (HES), and no significant decreased nodal efficiency was observed. The dysfunctional connections were mainly concentrated in the HES and prefrontal cortex. Furthermore, the altered nodal centrality of the MFG and abnormal functional connectivity in AIS were associated with patients' Mini-Mental State Examination scores. These results suggested that interrupted functional connectivity in language system organization after focal brain lesions could also result in disruptions in the topological organization of other brain circuits, and this may contribute to disturbances in cognition in AIS patients.

Investigating the correlation between crystallized IQ and network metrics in cerebellum using resting-state fMRI

Investigating the correlation between crystallized IQ and network metrics in cerebellum using resting-state fMRI

Disrupted modular architecture of cerebellum in schizophrenia: a graph theoretic analysis.

Recent studies of schizophrenia have revealed cognitive and memory deficits that are accompanied by disruptions of neuronal connectivity in cortical and subcortical brain regions. More recently, alterations of topological organization of structural networks in schizophrenia are also being identified using graph theoretical analysis. However, the role of the cerebellum in this network structure remains largely unknown. In this study, global network measures obtained from diffusion tensor imaging were computed in the cerebella of 25 patients with schizophrenia and 36 healthy volunteers. While cerebellar global network characteristics were slightly altered in schizophrenia patients compared with healthy controls, the patients showed a retained small-world network organization. The modular architecture, however, was changed mainly in crus II. Furthermore, schizophrenia patients had reduced correlations between modularity and microstructural integrity, as measured by fractional anisotropy (FA) in lobules I-IV and X. Finally, FA alterations were significantly correlated with the Positive and Negative Syndrome Scale symptom scores in schizophrenia patients. Taken together, our data suggest that schizophrenia patients have altered network architecture in the cerebellum with reduced local microstructural connectivity and that cerebellar structural abnormalities are associated symptoms of the disorder.

Extent of Bilateral Neuronal Network Reorganization and Functional Recovery in Relation to Stroke Severity

Remodeling of neuronal structures and networks is believed to significantly contribute to (partial) restoration of functions after stroke. However, it has been unclear to what extent the brain reorganizes and how this correlates with functional recovery in relation to stroke severity. We applied serial resting-state functional MRI and diffusion tensor imaging together with behavioral testing to relate longitudinal modifications in functional and structural connectivity of the sensorimotor neuronal network to changes in sensorimotor function after unilateral stroke in rats. We found that gradual improvement of functions is associated with wide-ranging changes in functional and structural connectivity within bilateral neuronal networks, particularly after large stroke. Both after medium and large stroke, brain reorganization eventually leads to (partial) normalization of neuronal signal synchronization within the affected sensorimotor cortical network (intraregional signal coherence), as well as between the affected and unaffected sensorimotor cortices (interhemispheric functional connectivity). Furthermore, the bilateral network configuration shifts from subacutely increased "small-worldness," possibly reflective of initial excessive neuronal clustering and wiring, toward a baseline small-world topology, optimal for global information transfer and local processing, at chronic stages. Cortical network remodeling was accompanied by recovery of initially disrupted structural integrity in corticospinal tract regions, which correlated positively with retrieval of sensorimotor functions. Our study demonstrates that the degree of functional recovery after stroke is associated with the extent of preservation or restoration of ipsilesional corticospinal tracts in combination with reinstatement of interhemispheric neuronal signal synchronization and normalization of small-world cortical network organization.

Globally Altered Structural Brain Network Topology in Grapheme-Color Synesthesia

Synesthesia is a perceptual phenomenon in which stimuli in one particular modality elicit a sensation within the same or another sensory modality (e.g., specific graphemes evoke the perception of particular colors). Grapheme-color synesthesia (GCS) has been proposed to arise from abnormal local cross-activation between grapheme and color areas because of their hyperconnectivity. Recently published studies did not confirm such a hyperconnectivity, although morphometric alterations were found in occipitotemporal, parietal, and frontal regions of synesthetes. We used magnetic resonance imaging surface-based morphometry and graph-theoretical network analyses to investigate the topology of structural brain networks in 24 synesthetes and 24 nonsynesthetes. Connectivity matrices were derived from region-wise cortical thickness correlations of 2366 different cortical parcellations across the whole cortex and from 154 more common brain divisions as well. Compared with nonsynesthetes, synesthetes revealed a globally altered structural network topology as reflected by reduced small-worldness, increased clustering, increased degree, and decreased betweenness centrality. Connectivity of the fusiform gyrus (FuG) and intraparietal sulcus (IPS) was changed as well. Hierarchical modularity analysis revealed increased intramodular and intermodular connectivity of the IPS in GCS. However, connectivity differences in the FuG and IPS showed a low specificity because of global changes. We provide first evidence that GCS is rooted in a reduced small-world network organization that is driven by increased clustering suggesting global hyperconnectivity within the synesthetes' brain. Connectivity alterations were widespread and not restricted to the FuG and IPS. Therefore, synesthetic experience might be only one phenotypic manifestation of the globally altered network architecture in GCS.

Aberrant Frontal and Temporal Complex Network Structure in Schizophrenia: A Graph Theoretical Analysis

Brain regions are not independent. They are interconnected by white matter tracts, together forming one integrative complex network. The topology of this network is crucial for efficient information integration between brain regions. Here, we demonstrate that schizophrenia involves an aberrant topology of the structural infrastructure of the brain network. Using graph theoretical analysis, complex structural brain networks of 40 schizophrenia patients and 40 human healthy controls were examined. Diffusion tensor imaging was used to reconstruct the white matter connections of the brain network, with the strength of the connections defined as the level of myelination of the tracts as measured through means of magnetization transfer ratio magnetic resonance imaging. Patients displayed a preserved overall small-world network organization, but focusing on specific brain regions and their capacity to communicate with other regions of the brain revealed significantly longer node-specific path lengths (higher L) of frontal and temporal regions, especially of bilateral inferior/superior frontal cortex and temporal pole regions. These findings suggest that schizophrenia impacts global network connectivity of frontal and temporal brain regions. Furthermore, frontal hubs of patients showed a significant reduction of betweenness centrality, suggesting a less central hub role of these regions in the overall network structure. Together, our findings suggest that schizophrenia patients have a less strongly globally integrated structural brain network with a reduced central role for key frontal hubs, resulting in a limited structural capacity to integrate information across brain regions.

The functional connectivity of different EEG bands moves towards small-world network organization during sleep

Objective To analyze the functional connectivity patterns of the different EEG bands during wakefulness and sleep (different sleep stages and cyclic alternating pattern (CAP) conditions), using concepts derived from Graph Theory. Methods We evaluated spatial patterns of EEG band synchronization between all possible pairs of electrodes (19) placed over the scalp of 10 sleeping healthy young normal subjects using two graph theoretical measures: the clustering coefficient (Cp) and the characteristic path length (Lp). The measures were obtained during wakefulness and the different sleep stages/CAP conditions from the real EEG connectivity networks and randomized control (surrogate) networks (Cp-s and Lp-s). Results We found values of Cp and Lp compatible with a small-world network organization in all sleep stages and for all EEG bands. All bands below 15 Hz showed an increase of these features during sleep (and during CAP-A phases in particular), compared to wakefulness. Conclusions The results of this study seem to confirm our initial hypothesis that during sleep there exists a clear trend for the functional connectivity of the EEG to move forward to an organization more similar to that of a small-world network, at least for the frequency bands lower than 15 Hz. Significance Sleep network “reconfiguration” might be one of the key mechanisms for the understanding of the “global” and “local” neural plasticity taking place during sleep.

O0011 The functional connectivity of EEG slow-wave activity during sleep has a small-world network organization

O0011 The functional connectivity of EEG slow-wave activity during sleep has a small-world network organization

Small-world network organization of functional connectivity of EEG slow-wave activity during sleep

ObjectiveTo analyze the functional connectivity patterns of the EEG slow-wave activity during the different sleep stages and Cyclic Alternating Pattern (CAP) conditions, using concepts derived from Graph Theory. MethodsWe evaluated spatial patterns of EEG slow-wave synchronization between all possible pairs of electrodes (19) placed over the scalp of 10 sleeping healthy young normal subjects using two graph theoretical measures: the clustering coefficient (Cp) and the characteristic path length (Lp). The measures were obtained during the different sleep stages and CAP conditions from the real EEG connectivity networks and randomized control (surrogate) networks (Cp-s and Lp-s). ResultsCp and Cp/Cp-s increased significantly from wakefulness to sleep while Lp and Lp/Lp-s did not show changes. Cp/Cp-s was higher for A1 phases, compared to B phases of CAP. ConclusionsThe network organization of the EEG slow-wave synchronization during sleep shows features characteristic of small-world networks (high Cp combined with low Lp); this type of organization is slightly but significantly more evident during the CAP A1 subtypes. SignificanceOur results show feasibility of using graph theoretical measures to characterize the complexity of brain networks during sleep and might indicate sleep, and the A1 phases of CAP in particular, as a period during which slow-wave synchronization shows optimal network organization for information processing.