Impaired small-world network efficiency and dynamic functional distribution in patients with cirrhosis

Hepatic encephalopathy (HE) is a complex neuropsychiatric syndrome and a major complication of liver cirrhosis. Dysmetabolism of the brain, related to elevated ammonia levels, interferes with intercortical connectivity and cognitive function. For evaluation of network efficiency, a 'small-world' network model can quantify the effectiveness of information transfer within brain networks. This study aimed to use small-world topology to investigate abnormalities of neuronal connectivity among widely distributed brain regions in patients with liver cirrhosis using resting-state functional magnetic resonance imaging (rs-fMRI). Seventeen cirrhotic patients without HE, 9 with minimal HE, 9 with overt HE, and 35 healthy controls were compared. The interregional correlation matrix was obtained by averaging the rs-fMRI time series over all voxels in each of the 90 regions using the automated anatomical labeling model. Cost and correlation threshold values were then applied to construct the functional brain network. The absolute and relative network efficiencies were calculated; quantifying distinct aspects of the local and global topological network organization. Correlations between network topology parameters, ammonia levels, and the severity of HE were determined using linear regression and ANOVA. The local and global topological efficiencies of the functional connectivity network were significantly disrupted in HE patients; showing abnormal small-world properties. Alterations in regional characteristics, including nodal efficiency and nodal strength, occurred predominantly in the association, primary, and limbic/paralimbic regions. The degree of network organization disruption depended on the severity of HE. Ammonia levels were also significantly associated with the alterations in local network properties. Results indicated that alterations in the rs-fMRI network topology of the brain were associated with HE grade; and that focal or diffuse lesions disturbed the functional network to further alter the global topology and efficiency of the whole brain network. These findings provide insights into the functional changes in the human brain in HE.     

Graph theoretical analysis of complex networks in the brain

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.     

Driving and driven architectures of directed small-world human brain functional networks

Recently, increasing attention has been focused on the investigation of the human brain connectome that describes the patterns of structural and functional connectivity networks of the human brain. Many studies of the human connectome have demonstrated that the brain network follows a small-world topology with an intrinsically cohesive modular structure and includes several network hubs in the medial parietal regions. However, most of these studies have only focused on undirected connections between regions in which the directions of information flow are not taken into account. How the brain regions causally influence each other and how the directed network of human brain is topologically organized remain largely unknown. Here, we applied linear multivariate Granger causality analysis (GCA) and graph theoretical approaches to a resting-state functional MRI dataset with a large cohort of young healthy participants (n = 86) to explore connectivity patterns of the population-based whole-brain functional directed network. This directed brain network exhibited prominent small-world properties, which obviously improved previous results of functional MRI studies showing weak small-world properties in the directed brain networks in terms of a kernel-based GCA and individual analysis. This brain network also showed significant modular structures associated with 5 well known subsystems: fronto-parietal, visual, paralimbic/limbic, subcortical and primary systems. Importantly, we identified several driving hubs predominantly located in the components of the attentional network (e.g., the inferior frontal gyrus, supplementary motor area, insula and fusiform gyrus) and several driven hubs predominantly located in the components of the default mode network (e.g., the precuneus, posterior cingulate gyrus, medial prefrontal cortex and inferior parietal lobule). Further split-half analyses indicated that our results were highly reproducible between two independent subgroups. The current study demonstrated the directions of spontaneous information flow and causal influences in the directed brain networks, thus providing new insights into our understanding of human brain functional connectome.     

Topological fractionation of resting-state networks

Exploring topological properties of human brain network has become an exciting topic in neuroscience research. Large-scale structural and functional brain networks both exhibit a small-world topology, which is evidence for global and local parallel information processing. Meanwhile, resting state networks (RSNs) underlying specific biological functions have provided insights into how intrinsic functional architecture influences cognitive and perceptual information processing. However, topological properties of single RSNs remain poorly understood. Here, we have two hypotheses: i) each RSN also has optimized small-world architecture; ii) topological properties of RSNs related to perceptual and higher cognitive processes are different. To test these hypotheses, we investigated the topological properties of the default-mode, dorsal attention, central-executive, somato-motor, visual and auditory networks derived from resting-state functional magnetic resonance imaging (fMRI). We found small-world topology in each RSN. Furthermore, small-world properties of cognitive networks were higher than those of perceptual networks. Our findings are the first to demonstrate a topological fractionation between perceptual and higher cognitive networks. Our approach may be useful for clinical research, especially for diseases that show selective abnormal connectivity in specific brain networks.     

Topological Organization of Functional Brain Networks in Healthy Children: Differences in Relation to Age,Sex, and Intelligence

Recent studies have demonstrated developmental changes of functional brain networks derived from functional connectivity using graph theoretical analysis, which has been rapidly translated to studies of brain network organization. However, little is known about sex- and IQ-related differences in the topological organization of functional brain networks during development. In this study, resting-state fMRI (rs-fMRI) was used to map the functional brain networks in 51 healthy children. We then investigated the effects of age, sex, and IQ on economic small-world properties and regional nodal properties of the functional brain networks. At a global level of whole networks, we found significant age-related increases in the small-worldness and local efficiency, significant higher values of the global efficiency in boys compared with girls, and no significant IQ-related difference. Age-related increases in the regional nodal properties were found predominately in the frontal brain regions, whereas the parietal, temporal, and occipital brain regions showed age-related decreases. Significant sex-related differences in the regional nodal properties were found in various brain regions, primarily related to the default mode, language, and vision systems. Positive correlations between IQ and the regional nodal properties were found in several brain regions related to the attention system, whereas negative correlations were found in various brain regions primarily involved in the default mode, emotion, and language systems. Together, our findings of the network topology of the functional brain networks in healthy children and its relationship with age, sex, and IQ bring new insights into the understanding of brain maturation and cognitive development during childhood and adolescence.     

Disturbed Small-World Networks and Neurocognitive Function in Frontal Lobe Low-Grade Glioma Patients

Background

Brain tumor patients often associated with losses of the small-world configuration and neurocognitive functions before operations. However, few studies were performed on the impairments of frontal lobe low-grade gliomas (LGG) after tumor resection using small-world network features.

Methodology/Principal Findings

To detect differences in the whole brain topology among LGG patients before and after operation, a combined study of neurocognitive assessment and graph theoretical network analysis of fMRI data was performed. We collected resting-state fMRI data of 12 carefully selected frontal lobe LGG patients before and after operation. We calculated the topological properties of brain functional networks in the 12 LGG, and compared with 12 healthy controls (HCs). We also applied Montreal Cognitive Assessment (MoCA) in a subset of patients (n = 12, including before and after operation groups) and HCs (n = 12). The resulting functional connectivity matrices were constructed for all 12 patients, and binary network analysis was performed. In the range of , the functional networks in preoperative LGG and postoperative one both fitted the definition of small-worldness. We proposed as small-world network interval, and the results showed that the topological properties were found to be disrupted in the two LGG groups, meanwhile the global efficiency increased and the local efficiency decreased. in the two LGG groups both were longer than HCs. in the LGG groups were smaller than HCs. Compared with the Hcs, MoCA in the two LGG groups were lower than HCs with significant difference, and the disturbed networks in the LGG were negatively related to worse MoCA scores.

Conclusions

Disturbed small-worldness preperty in the two LGG groups was found and widely spread in the strength and spatial organization of brain networks, and the alterated small-world network may be responsible for cognitive dysfunction in frontal lobe LGG patients.     

Network analysis of intrinsic functional brain connectivity in Alzheimer's disease

Functional brain networks detected in task-free (“resting-state”) functional magnetic resonance imaging (fMRI) have a small-world architecture that reflects a robust functional organization of the brain. Here, we examined whether this functional organization is disrupted in Alzheimer's disease (AD). Task-free fMRI data from 21 AD subjects and 18 age-matched controls were obtained. Wavelet analysis was applied to the fMRI data to compute frequency-dependent correlation matrices. Correlation matrices were thresholded to create 90-node undirected-graphs of functional brain networks. Small-world metrics (characteristic path length and clustering coefficient) were computed using graph analytical methods. In the low frequency interval 0.01 to 0.05 Hz, functional brain networks in controls showed small-world organization of brain activity, characterized by a high clustering coefficient and a low characteristic path length. In contrast, functional brain networks in AD showed loss of small-world properties, characterized by a significantly lower clustering coefficient (p<0.01), indicative of disrupted local connectivity. Clustering coefficients for the left and right hippocampus were significantly lower (p<0.01) in the AD group compared to the control group. Furthermore, the clustering coefficient distinguished AD participants from the controls with a sensitivity of 72% and specificity of 78%. Our study provides new evidence that there is disrupted organization of functional brain networks in AD. Small-world metrics can characterize the functional organization of the brain in AD, and our findings further suggest that these network measures may be useful as an imaging-based biomarker to distinguish AD from healthy aging.     

Abnormal Organization of White Matter Network in Patients with No Dementia after Ischemic Stroke

Structural changes after ischemic stroke could affect information communication extensively in the brain network. It is likely that the defects in the white matter (WM) network play a key role in information interchange. In this study, we used graph theoretical analysis to examine potential organization alteration in the WM network architecture derived from diffusion tensor images from subjects with no dementia and experienced stroke in the past 5.4–14.8 months (N = 47, Mini-Mental Screening Examination, MMSE range 18–30), compared with a normal control group with 44 age and gender-matched healthy volunteers (MMSE range 26–30). Region-wise connectivity was derived from fiber connection density of 90 different cortical and subcortical parcellations across the whole brain. Both normal controls and patients with chronic stroke exhibited efficient small-world properties in their WM structural networks. Compared with normal controls, topological efficiency was basically unaltered in the patients with chronic stroke, as reflected by unchanged local and global clustering coefficient, characteristic path length, and regional efficiency. No significant difference in hub distribution was found between normal control and patient groups. Patients with chronic stroke, however, were found to have reduced betweenness centrality and predominantly located in the orbitofrontal cortex, whereas increased betweenness centrality and vulnerability were observed in parietal-occipital cortex. The National Institutes of Health Stroke Scale (NIHSS) score of patient is correlated with the betweenness centrality of right pallidum and local clustering coefficient of left superior occipital gyrus. Our findings suggest that patients with chronic stroke still exhibit efficient small-world organization and unaltered topological efficiency, with altered topology at orbitofrontal cortex and parietal-occipital cortex in the overall structural network. Findings from this study could help in understanding the mechanism of cognitive impairment and functional compensation occurred in patients with chronic stroke.     

Emergence of a small-world functional network in cultured neurons

The functional networks of cultured neurons exhibit complex network properties similar to those found in vivo. Starting from random seeding, cultures undergo significant reorganization during the initial period in vitro, yet despite providing an ideal platform for observing developmental changes in neuronal connectivity, little is known about how a complex functional network evolves from isolated neurons. In the present study, evolution of functional connectivity was estimated from correlations of spontaneous activity. Network properties were quantified using complex measures from graph theory and used to compare cultures at different stages of development during the first 5 weeks in vitro. Networks obtained from young cultures (14 days in vitro) exhibited a random topology, which evolved to a small-world topology during maturation. The topology change was accompanied by an increased presence of highly connected areas (hubs) and network efficiency increased with age. The small-world topology balances integration of network areas with segregation of specialized processing units. The emergence of such network structure in cultured neurons, despite a lack of external input, points to complex intrinsic biological mechanisms. Moreover, the functional network of cultures at mature ages is efficient and highly suited to complex processing tasks.     

Altered small-world brain networks in schizophrenia patients during working memory performance

Impairment of working memory (WM) performance in schizophrenia patients (SZ) is well-established. Compared to healthy controls (HC), SZ patients show aberrant blood oxygen level dependent (BOLD) activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI) data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP) at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs) defined by group independent component analysis (ICA). The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1) at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2) in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3) the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.     

Exploring local structural organization of metabolic networks using subgraph patterns

Metabolic networks of many cellular organisms share global statistical features. Their connectivity distributions follow the long-tailed power law and show the small-world property. In addition, their modular structures are organized in a hierarchical manner. Although the global topological organization of metabolic networks is well understood, their local structural organization is still not clear. Investigating local properties of metabolic networks is necessary to understand the nature of metabolism in living organisms. To identify the local structural organization of metabolic networks, we analysed the subgraphs of metabolic networks of 43 organisms from three domains of life. We first identified the network motifs of metabolic networks and identified the statistically significant subgraph patterns. We then compared metabolic networks from different domains and found that they have similar local structures and that the local structure of each metabolic network has its own taxonomical meaning. Organisms closer in taxonomy showed similar local structures. In addition, the common substrates of 43 metabolic networks were not randomly distributed, but were more likely to be constituents of cohesive subgraph patterns.     

Abnormal reorganization of functional cortical small-world networks in focal hand dystonia

We investigated the large-scale functional cortical connectivity network in focal hand dystonia (FHD) patients using graph theoretic measures to assess efficiency. High-resolution EEGs were recorded in 15 FHD patients and 15 healthy volunteers at rest and during a simple sequential finger tapping task. Mutual information (MI) values of wavelet coefficients were estimated to create an association matrix between EEG electrodes, and to produce a series of adjacency matrices or graphs, G, by thresholding with network cost. Efficiency measures of small-world networks were assessed. As a result, we found that FHD patients have economical small-world properties in their brain functional networks in the alpha and beta bands. During a motor task, in the beta band network, FHD patients have decreased efficiency of small-world networks, whereas healthy volunteers increase efficiency. Reduced efficient beta band network in FHD patients during the task was consistently observed in global efficiency, cost-efficiency, and maximum cost-efficiency. This suggests that the beta band functional cortical network of FHD patients is reorganized even during a task that does not induce dystonic symptoms, representing a loss of long-range communication and abnormal functional integration in large-scale brain functional cortical networks. Moreover, negative correlations between efficiency measures and duration of disease were found, indicating that the longer duration of disease, the less efficient the beta band network in FHD patients. In regional efficiency analysis, FHD patients at rest have high regional efficiency at supplementary motor cortex (SMA) compared with healthy volunteers; however, it is diminished during the motor task, possibly reflecting abnormal inhibition in FHD patients. The present study provides the first evidence with graph theory for abnormal reconfiguration of brain functional networks in FHD during motor task.     

Comparing structural and functional graph theory features in the human brain using multimodal MRI

Recent advances in magnetic resonance imaging (MRI) are allowing neuroscientists to gain critical insights into the neural networks mediating a variety of cognitive processes. This work investigates structural and functional connectivity in the human brain under different experimental conditions through multimodal MRI acquisitions. To define the nodes of a full-brain network, a set of regions was identified from resting-state functional MRI (fMRI) data using spatial independent component analysis (sICA) and a hierarchical clustering technique. Diffusion-weighted imaging (DWI) data were acquired from the same subjects and a probabilistic fiber tracking method was used to estimate the structure of this network. Using features originating from graph theory, such as small-world properties and network efficiency, we characterized the structural and functional connectivities of the full-brain network and we compared them quantitatively. We showed that structural and functional networks shared some properties in terms of topology as measured by the distribution of the node degrees, hence supporting the existence of an underlying anatomical substrate for functional networks.     

Using Pareto optimality to explore the topology and dynamics of the human connectome

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain''s topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an ‘economical’ small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.     

Rich Club Organization of Macaque Cerebral Cortex and Its Role in Network Communication

Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.     

Altered small-world,functional brain networks in patients with lower back pain

In this study, we aimed to investigate the functional network changes that occur in patients with lower back pain(LBP). We also investigated the link between LBP and the small-world properties of functional networks within the brain. Functional MRI(fMRI) was performed on 20 individuals with LBP and 17 age and gender-matched normal controls during the resting state. The severity of the pain in the individuals with LBP ranged from 5 to 8 on a 0–10 scale, with 0 indicating no pain. Network-based statistics were performed to investigate the differences between the brain networks of individuals with LBP and those of normal controls. Several small-world parameters of brain networks were calculated, including the clustering coefficient, characteristic path length, local efficiency, and global efficiency. These criteria reflect the overall network efficiency. The brain networks in the individuals with LBP due to herniation of a lumbar disc demonstrated a significantly longer characteristic path length as well as a lower clustering coefficient, global efficiency, and local efficiency compared to those in control subjects. We found that LBP patients tended to have unstable and inefficient brain networks when compared with healthy controls. In addition, LBP individuals showed significantly decreased functional connectivity in the anterior cingulate cortex, middle cingulate cortex, post cingulate cortex, inferior frontal gyrus, middle temporal gyrus, occipital gyrus, postcentral gyrus, precentral gyrus, supplementary motor area, thalamus, fusiform, caudate, and cerebellum. We believe that these regions may be involved in the pathophysiology of lower back pain.     

Efficiency and cost of economical brain functional networks

Brain anatomical networks are sparse, complex, and have economical small-world properties. We investigated the efficiency and cost of human brain functional networks measured using functional magnetic resonance imaging (fMRI) in a factorial design: two groups of healthy old (N = 11; mean age = 66.5 years) and healthy young (N = 15; mean age = 24.7 years) volunteers were each scanned twice in a no-task or “resting” state following placebo or a single dose of a dopamine receptor antagonist (sulpiride 400 mg). Functional connectivity between 90 cortical and subcortical regions was estimated by wavelet correlation analysis, in the frequency interval 0.06–0.11 Hz, and thresholded to construct undirected graphs. These brain functional networks were small-world and economical in the sense of providing high global and local efficiency of parallel information processing for low connection cost. Efficiency was reduced disproportionately to cost in older people, and the detrimental effects of age on efficiency were localised to frontal and temporal cortical and subcortical regions. Dopamine antagonism also impaired global and local efficiency of the network, but this effect was differentially localised and did not interact with the effect of age. Brain functional networks have economical small-world properties—supporting efficient parallel information transfer at relatively low cost—which are differently impaired by normal aging and pharmacological blockade of dopamine transmission.     

Intra- and Inter-Frequency Brain Network Structure in Health and Schizophrenia

Empirical studies over the past two decades have provided support for the hypothesis that schizophrenia is characterized by altered connectivity patterns in functional brain networks. These alterations have been proposed as genetically mediated diagnostic biomarkers and are thought to underlie altered cognitive functions such as working memory. However, the nature of this dysconnectivity remains far from understood. In this study, we perform an extensive analysis of functional connectivity patterns extracted from MEG data in 14 subjects with schizophrenia and 14 healthy controls during a 2-back working memory task. We investigate uni-, bi- and multivariate properties of sensor time series by computing wavelet entropy of and correlation between time series, and by constructing binary networks of functional connectivity both within and between classical frequency bands (, , , and ). Networks are based on the mutual information between wavelet time series, and estimated for each trial window separately, enabling us to consider both network topology and network dynamics. We observed significant decreases in time series entropy and significant increases in functional connectivity in the schizophrenia group in comparison to the healthy controls and identified an inverse relationship between these measures across both subjects and sensors that varied over frequency bands and was more pronounced in controls than in patients. The topological organization of connectivity was altered in schizophrenia specifically in high frequency and band networks as well as in the - cross-frequency networks. Network topology varied over trials to a greater extent in patients than in controls, suggesting disease-associated alterations in dynamic network properties of brain function. Our results identify signatures of aberrant neurophysiological behavior in schizophrenia across uni-, bi- and multivariate scales and lay the groundwork for further clinical studies that might lead to the discovery of new intermediate phenotypes.     

Emergent functional properties of neuronal networks with controlled topology

The interplay between anatomical connectivity and dynamics in neural networks plays a key role in the functional properties of the brain and in the associated connectivity changes induced by neural diseases. However, a detailed experimental investigation of this interplay at both cellular and population scales in the living brain is limited by accessibility. Alternatively, to investigate the basic operational principles with morphological, electrophysiological and computational methods, the activity emerging from large in vitro networks of primary neurons organized with imposed topologies can be studied. Here, we validated the use of a new bio-printing approach, which effectively maintains the topology of hippocampal cultures in vitro and investigated, by patch-clamp and MEA electrophysiology, the emerging functional properties of these grid-confined networks. In spite of differences in the organization of physical connectivity, our bio-patterned grid networks retained the key properties of synaptic transmission, short-term plasticity and overall network activity with respect to random networks. Interestingly, the imposed grid topology resulted in a reinforcement of functional connections along orthogonal directions, shorter connectivity links and a greatly increased spiking probability in response to focal stimulation. These results clearly demonstrate that reliable functional studies can nowadays be performed on large neuronal networks in the presence of sustained changes in the physical network connectivity.