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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.

Modularity is a fundamental concept in systems neuroscience, referring to the formation of local cliques or modules of densely intra-connected nodes that are sparsely inter-connected with nodes in other modules. Topological modularity of brain functional networks can quantify theoretically anticipated abnormality of brain network community structure – so-called dysmodularity – in developmental disorders such as childhood-onset schizophrenia (COS). We used graph theory to investigate topology of networks derived from resting-state fMRI data on 13 COS patients and 19 healthy volunteers. We measured functional connectivity between each pair of 100 regional nodes, focusing on wavelet correlation in the frequency interval 0.05–0.1 Hz, then applied global and local thresholding rules to construct graphs from each individual association matrix over the full range of possible connection densities. We show how local thresholding based on the minimum spanning tree facilitates group comparisons of networks by forcing the connectedness of sparse graphs. Threshold-dependent graph theoretical results are compatible with the results of a k-means unsupervised learning algorithm and a multi-resolution (spin glass) approach to modularity, both of which also find community structure but do not require thresholding of the association matrix. In general modularity of brain functional networks was significantly reduced in COS, due to a relatively reduced density of intra-modular connections between neighboring regions. Other network measures of local organization such as clustering were also decreased, while complementary measures of global efficiency and robustness were increased, in the COS group. The group differences in complex network properties were mirrored by differences in simpler statistical properties of the data, such as the variability of the global time series and the internal homogeneity of the time series within anatomical regions of interest.

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.

In recent years, graph theoretical analyses of neuroimaging data have increased our understanding of the organization of large-scale structural and functional brain networks. However, tools for pipeline application of graph theory for analyzing topology of brain networks is still lacking. In this report, we describe the development of a graph-analysis toolbox (GAT) that facilitates analysis and comparison of structural and functional network brain networks. GAT provides a graphical user interface (GUI) that facilitates construction and analysis of brain networks, comparison of regional and global topological properties between networks, analysis of network hub and modules, and analysis of resilience of the networks to random failure and targeted attacks. Area under a curve (AUC) and functional data analyses (FDA), in conjunction with permutation testing, is employed for testing the differences in network topologies; analyses that are less sensitive to the thresholding process. We demonstrated the capabilities of GAT by investigating the differences in the organization of regional gray-matter correlation networks in survivors of acute lymphoblastic leukemia (ALL) and healthy matched Controls (CON). The results revealed an alteration in small-world characteristics of the brain networks in the ALL survivors; an observation that confirm our hypothesis suggesting widespread neurobiological injury in ALL survivors. Along with demonstration of the capabilities of the GAT, this is the first report of altered large-scale structural brain networks in ALL survivors.

Background

Although focal epilepsies are increasingly recognized to affect multiple and remote neural systems, the underlying spatiotemporal pattern and the relationships between recurrent spontaneous seizures, global functional connectivity, and structural integrity remain largely unknown.

Methodology/Principal Findings

Here we utilized serial resting-state functional MRI, graph-theoretical analysis of complex brain networks and diffusion tensor imaging to characterize the evolution of global network topology, functional connectivity and structural changes in the interictal brain in relation to focal epilepsy in a rat model. Epileptic networks exhibited a more regular functional topology than controls, indicated by a significant increase in shortest path length and clustering coefficient. Interhemispheric functional connectivity in epileptic brains decreased, while intrahemispheric functional connectivity increased. Widespread reductions of fractional anisotropy were found in white matter regions not restricted to the vicinity of the epileptic focus, including the corpus callosum.

Conclusions/Significance

Our longitudinal study on the pathogenesis of network dynamics in epileptic brains reveals that, despite the locality of the epileptogenic area, epileptic brains differ in their global network topology, connectivity and structural integrity from healthy brains.

Background

Although a large body of knowledge about both brain structure and function has been gathered over the last decades, we still have a poor understanding of their exact relationship. Graph theory provides a method to study the relation between network structure and function, and its application to neuroscientific data is an emerging research field. We investigated topological changes in large-scale functional brain networks in patients with Alzheimer's disease (AD) and frontotemporal lobar degeneration (FTLD) by means of graph theoretical analysis of resting-state EEG recordings. EEGs of 20 patients with mild to moderate AD, 15 FTLD patients, and 23 non-demented individuals were recorded in an eyes-closed resting-state. The synchronization likelihood (SL), a measure of functional connectivity, was calculated for each sensor pair in 0.5–4 Hz, 4–8 Hz, 8–10 Hz, 10–13 Hz, 13–30 Hz and 30–45 Hz frequency bands. The resulting connectivity matrices were converted to unweighted graphs, whose structure was characterized with several measures: mean clustering coefficient (local connectivity), characteristic path length (global connectivity) and degree correlation (network 'assortativity'). All results were normalized for network size and compared with random control networks.

Results

In AD, the clustering coefficient decreased in the lower alpha and beta bands (p < 0.001), and the characteristic path length decreased in the lower alpha and gamma bands (p < 0.05) compared to controls. In FTLD no significant differences with controls were found in these measures. The degree correlation decreased in both alpha bands in AD compared to controls (p < 0.05), but increased in the FTLD lower alpha band compared with controls (p < 0.01).

Conclusion

With decreasing local and global connectivity parameters, the large-scale functional brain network organization in AD deviates from the optimal 'small-world' network structure towards a more 'random' type. This is associated with less efficient information exchange between brain areas, supporting the disconnection hypothesis of AD. Surprisingly, FTLD patients show changes in the opposite direction, towards a (perhaps excessively) more 'ordered' network structure, possibly reflecting a different underlying pathophysiological process.

Purpose of review

Recent developments in the statistical physics of complex networks have been translated to neuroimaging data in an effort to enhance our understanding of human brain structural and functional networks. This review focuses on studies using graph theoretical measures applied to structural MRI, diffusion MRI, functional MRI, electroencephalography and magnetoencephalography data.

Recent findings

Complex network properties have been identified with some consistency in all modalities of neuroimaging data and over a range of spatial and time scales. Conserved properties include small-worldness, high efficiency of information transfer for low wiring cost, modularity, and the existence of network hubs. Structural and functional network metrics have been found to be heritable and to change with normal aging. Clinical studies, principally in Alzheimer’s disease and schizophrenia, have identified abnormalities of network configuration in patients. Future work will likely involve efforts to synthesize structural and functional networks in integrated models and to explore the inter-dependence of network configuration and cognitive performance.

Summary

Graph theoretical analysis of neuroimaging data is growing rapidly and could potentially provide a relatively simple but powerful quantitative framework to describe and compare whole human brain structural and functional networks under diverse experimental and clinical conditions.

The characterization of the topological architecture of complex networks underlying the structural and functional organization of the brain is a basic challenge in neuroscience. However, direct evidence for anatomical connectivity networks in the human brain remains scarce. Here, we utilized diffusion tensor imaging deterministic tractography to construct a macroscale anatomical network capturing the underlying common connectivity pattern of human cerebral cortex in a large sample of subjects (80 young adults) and further quantitatively analyzed its topological properties with graph theoretical approaches. The cerebral cortex was divided into 78 cortical regions, each representing a network node, and 2 cortical regions were considered connected if the probability of fiber connections exceeded a statistical criterion. The topological parameters of the established cortical network (binarized) resemble that of a “small-world” architecture characterized by an exponentially truncated power-law distribution. These characteristics imply high resilience to localized damage. Furthermore, this cortical network was characterized by major hub regions in association cortices that were connected by bridge connections following long-range white matter pathways. Our results are compatible with previous structural and functional brain networks studies and provide insight into the organizational principles of human brain anatomical networks that underlie functional states.

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.

Alzheimer’s disease (AD) is the most common form of dementia. As an incurable, progressive, and neurodegenerative disease, it causes cognitive and memory deficits. However, the biological mechanisms underlying the disease are not thoroughly understood. In recent years, non-invasive neuroimaging and neurophysiological techniques [e.g., structural magnetic resonance imaging (MRI), diffusion MRI, functional MRI, and EEG/MEG] and graph theory based network analysis have provided a new perspective on structural and functional connectivity patterns of the human brain (i.e., the human connectome) in health and disease. Using these powerful approaches, several recent studies of patients with AD exhibited abnormal topological organization in both global and regional properties of neuronal networks, indicating that AD not only affects specific brain regions, but also alters the structural and functional associations between distinct brain regions. Specifically, disruptive organization in the whole-brain networks in AD is involved in the loss of small-world characters and the re-organization of hub distributions. These aberrant neuronal connectivity patterns were associated with cognitive deficits in patients with AD, even with genetic factors in healthy aging. These studies provide empirical evidence to support the existence of an aberrant connectome of AD. In this review we will summarize recent advances discovered in large-scale brain network studies of AD, mainly focusing on graph theoretical analysis of brain connectivity abnormalities. These studies provide novel insights into the pathophysiological mechanisms of AD and could be helpful in developing imaging biomarkers for disease diagnosis and monitoring.

The complex organization of connectivity in the human brain is incompletely understood. Recently, topological measures based on graph theory have provided a new approach to quantify large-scale cortical networks. These methods have been applied to anatomical connectivity data on non-human species and cortical networks have been shown to have small-world topology, associated with high local and global efficiency of information transfer. Anatomical networks derived from cortical thickness measurements have shown the same organizational properties of the healthy human brain, consistent with similar results reported in functional networks derived from resting state functional MRI and MEG data. Here we show, using anatomical networks derived from analysis of inter-regional covariation of gray matter volume in magnetic resonance imaging (MRI) data on 259 healthy volunteers, that classical divisions of cortex (multimodal, unimodal and transmodal) have some distinct topological attributes. While all cortical divisions shared non-random properties of small-worldness and efficient wiring (short mean Euclidean distance between connected regions), the multimodal network had a hierarchical organization, dominated by frontal hubs with low clustering, whereas the transmodal network was assortative. Moreover, in a sample of 203 people with schizophrenia, multimodal network organization was abnormal, as indicated by reduced hierarchy, the loss of frontal and the emergence of non-frontal hubs, and increased connection distance. We propose that the topological differences between divisions of normal cortex may represent the outcome of different growth processes for multimodal and transmodal networks; and that neurodevelopmental abnormalities in schizophrenia specifically impact multimodal cortical organization.

Background

Little is known about the changes of brain structural and functional connectivity networks underlying the pathophysiology in migraine. We aimed to investigate how the cortical network reorganization is altered by frequent cortical overstimulation associated with migraine.

Methodology/Principal Findings

Gray matter volumes and resting-state functional magnetic resonance imaging signal correlations were employed to construct structural and functional networks between brain regions in 43 female patients with migraine (PM) and 43 gender-matched healthy controls (HC) by using graph theory-based approaches. Compared with the HC group, the patients showed abnormal global topology in both structural and functional networks, characterized by higher mean clustering coefficients without significant change in the shortest absolute path length, which indicated that the PM lost optimal topological organization in their cortical networks. Brain hubs related to pain-processing revealed abnormal nodal centrality in both structural and functional networks, including the precentral gyrus, orbital part of the inferior frontal gyrus, parahippocampal gyrus, anterior cingulate gyrus, thalamus, temporal pole of the middle temporal gyrus and the inferior parietal gyrus. Negative correlations were found between migraine duration and regions with abnormal centrality. Furthermore, the dysfunctional connections in patients' cortical networks formed into a connected component and three dysregulated modules were identified involving pain-related information processing and motion-processing visual networks.

Conclusions

Our results may reflect brain alteration dynamics resulting from migraine and suggest that long-term and high-frequency headache attacks may cause both structural and functional connectivity network reorganization. The disrupted information exchange between brain areas in migraine may be reshaped into a hierarchical modular structure progressively.

Although metaphorical and conceptual connections between the human brain and the financial markets have often been drawn, rigorous physical or mathematical underpinnings of this analogy remain largely unexplored. Here, we apply a statistical and graph theoretic approach to the study of two datasets – the time series of 90 stocks from the New York stock exchange over a 3-year period, and the fMRI-derived time series acquired from 90 brain regions over the course of a 10-min-long functional MRI scan of resting brain function in healthy volunteers. Despite the many obvious substantive differences between these two datasets, graphical analysis demonstrated striking commonalities in terms of global network topological properties. Both the human brain and the market networks were non-random, small-world, modular, hierarchical systems with fat-tailed degree distributions indicating the presence of highly connected hubs. These properties could not be trivially explained by the univariate time series statistics of stock price returns. This degree of topological isomorphism suggests that brains and markets can be regarded broadly as members of the same family of networks. The two systems, however, were not topologically identical. The financial market was more efficient and more modular – more highly optimized for information processing – than the brain networks; but also less robust to systemic disintegration as a result of hub deletion. We conclude that the conceptual connections between brains and markets are not merely metaphorical; rather these two information processing systems can be rigorously compared in the same mathematical language and turn out often to share important topological properties in common to some degree. There will be interesting scientific arbitrage opportunities in further work at the graph-theoretically mediated interface between systems neuroscience and the statistical physics of financial markets.

Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data.

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a “fingerprint”. Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the “uncertainty” of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.

Abnormalities in the topology of brain networks may be an important feature and etiological factor for psychogenic non-epileptic seizures (PNES). To explore this possibility, we applied a graph theoretical approach to functional networks based on resting state EEGs from 13 PNES patients and 13 age- and gender-matched controls. The networks were extracted from Laplacian-transformed time-series by a cross-correlation method. PNES patients showed close to normal local and global connectivity and small-world structure, estimated with clustering coefficient, modularity, global efficiency, and small-worldness (SW) metrics, respectively. Yet the number of PNES attacks per month correlated with a weakness of local connectedness and a skewed balance between local and global connectedness quantified with SW, all in EEG alpha band. In beta band, patients demonstrated above-normal resiliency, measured with assortativity coefficient, which also correlated with the frequency of PNES attacks. This interictal EEG phenotype may help improve differentiation between PNES and epilepsy. The results also suggest that local connectivity could be a target for therapeutic interventions in PNES. Selective modulation (strengthening) of local connectivity might improve the skewed balance between local and global connectivity and so prevent PNES events.

In the past decade, resting-state functional MRI (R-fMRI) measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain's spontaneous or intrinsic (i.e., task-free) activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain's intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging, and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.

The topological architecture of the cerebral anatomical network reflects the structural organization of the human brain. Recently, topological measures based on graph theory have provided new approaches for quantifying large-scale anatomical networks. Diffusion MRI studies have revealed the efficient small-world properties and modular structure of the anatomical network in normal subjects. However, no previous study has used diffusion MRI to reveal changes in the brain anatomical network in early blindness. Here, we utilized diffusion tensor imaging to construct binary anatomical networks for 17 early blind subjects and 17 age- and gender-matched sighted controls. We established the existence of structural connections between any pair of the 90 cortical and sub-cortical regions using deterministic tractography. Compared with controls, early blind subjects showed a decreased degree of connectivity, a reduced global efficiency, and an increased characteristic path length in their brain anatomical network, especially in the visual cortex. Moreover, we revealed some regions with motor or somatosensory function have increased connections with other brain regions in the early blind, which suggested experience-dependent compensatory plasticity. This study is the first to show alterations in the topological properties of the anatomical network in early blindness. From the results, we suggest that analyzing the brain's anatomical network obtained using diffusion MRI data provides new insights into the understanding of the brain's re-organization in the specific population with early visual deprivation.

In recent years, a large number of human studies have investigated large-scale network properties of the brain, typically during the resting state. A critical gap in the knowledge base concerns the understanding of network properties of a focused set of brain regions during task conditions engaging these regions. Although emotion and motivation recruit many brain regions, it is currently unknown how they affect network-level properties of inter-region interactions. In the present study, we sought to characterize network structure during “mini-states” engendered by emotional and motivational cues investigated in separate studies. To do so, we employed graph-theoretic network analysis to probe network-, community-, and node-level properties of the trial-by-trial functional connectivity between regions of interest. We employed methods that operate on weighted graphs that make use of the continuous information of connectivity strength. In both the Emotion and Motivation datasets, global efficiency increased and decomposability decreased. Thus, processing became less segregated with the context signaled by the cue (potential shock or potential reward). Our findings also revealed several important features of inter-community communication, including notable contributions of the bed nucleus of the stria terminalis, anterior insula, and thalamus during threat, and of the caudate and nucleus accumbens during reward. Together, the results suggest that one way in which emotional and motivational processing affect brain responses is by enhancing signal communication between regions, especially between cortical and subcortical ones.

Modern imaging methods allow a non-invasive assessment of both structural and functional brain connectivity. This has lead to the identification of disease-related alterations affecting functional connectivity. The mechanism of how such alterations in functional connectivity arise in a structured network of interacting neural populations is as yet poorly understood. Here we use a modeling approach to explore the way in which this can arise and to highlight the important role that local population dynamics can have in shaping emergent spatial functional connectivity patterns. The local dynamics for a neural population is taken to be of the Wilson–Cowan type, whilst the structural connectivity patterns used, describing long-range anatomical connections, cover both realistic scenarios (from the CoComac database) and idealized ones that allow for more detailed theoretical study. We have calculated graph–theoretic measures of functional network topology from numerical simulations of model networks. The effect of the form of local dynamics on the observed network state is quantified by examining the correlation between structural and functional connectivity. We document a profound and systematic dependence of the simulated functional connectivity patterns on the parameters controlling the dynamics. Importantly, we show that a weakly coupled oscillator theory explaining these correlations and their variation across parameter space can be developed. This theoretical development provides a novel way to characterize the mechanisms for the breakdown of functional connectivity in diseases through changes in local dynamics.

This article presents the integration of brain injury biomechanics and graph theoretical analysis of neuronal connections, or connectomics, to form a neurocomputational model that captures spatiotemporal characteristics of trauma. We relate localized mechanical brain damage predicted from biofidelic finite element simulations of the human head subjected to impact with degradation in the structural connectome for a single individual. The finite element model incorporates various length scales into the full head simulations by including anisotropic constitutive laws informed by diffusion tensor imaging. Coupling between the finite element analysis and network-based tools is established through experimentally-based cellular injury thresholds for white matter regions. Once edges are degraded, graph theoretical measures are computed on the “damaged” network. For a frontal impact, the simulations predict that the temporal and occipital regions undergo the most axonal strain and strain rate at short times (less than 24 hrs), which leads to cellular death initiation, which results in damage that shows dependence on angle of impact and underlying microstructure of brain tissue. The monotonic cellular death relationships predict a spatiotemporal change of structural damage. Interestingly, at 96 hrs post-impact, computations predict no network nodes were completely disconnected from the network, despite significant damage to network edges. At early times () network measures of global and local efficiency were degraded little; however, as time increased to 96 hrs the network properties were significantly reduced. In the future, this computational framework could help inform functional networks from physics-based structural brain biomechanics to obtain not only a biomechanics-based understanding of injury, but also neurophysiological insight.

Author Summary

According to the Centers for Disease Control and Prevention in the United States, approximately 1.7 million people, on average, sustain a traumatic brain injury annually. During the last few decades, brain neurotrauma biomechanics has been an active area of research involving medical clinicians and a broad range of scientists and engineers. In addition, advances and fast growth of human connectomics continues to reveal new insights into the damaged brain. With recent advances in computational methods and high performance computing, we see the need and the exciting possibility to merge brain neurotrauma biomechanics and human connectomics science to form a new area of investigation - connectome neurotrauma mechanics. For neurotrauma, the idea is simple - inform human structural connectome analysis using physics-based predictions of biomechanical brain injury. If successful, this technique may be further used to inform human functional connectome analysis, thus providing a new tool to help understand the pathophysiology of mild traumatic brain injury.

Background

Migraine shows gender-specific incidence and has a higher prevalence in females. However, little is known about gender-related differences in dysfunctional brain organization, which may account for gender-specific vulnerability and characteristics of migraine. In this study, we considered gender-related differences in the topological property of resting functional networks.

Methodology/Principal Findings

Data was obtained from 38 migraine patients (18 males and 20 females) and 38 healthy subjects (18 males and 20 females). We used the graph theory analysis, which becomes a powerful tool in investigating complex brain networks on a whole brain scale and could describe functional interactions between brain regions. Using this approach, we compared the brain functional networks between these two groups, and several network properties were investigated, such as small-worldness, network resilience, nodal centrality, and interregional connections. In our findings, these network characters were all disrupted in patients suffering from chronic migraine. More importantly, these functional damages in the migraine-affected brain had a skewed balance between males and females. In female patients, brain functional networks showed worse resilience, more regions exhibited decreased nodal centrality, and more functional connections revealed abnormalities than in male patients.

Conclusions

These results indicated that migraine may have an additional influence on females and lead to more dysfunctional organization in their resting functional networks.

Aging is accompanied by substantial changes in brain function, including functional reorganization of large-scale brain networks. Such differences in network architecture have been reported both at rest and during cognitive task performance, but an open question is whether these age-related differences show task-dependent effects or represent only task-independent changes attributable to a common factor (i.e., underlying physiological decline). To address this question, we used graph theoretic analysis to construct weighted cortical functional networks from hemodynamic (functional MRI) responses in 12 younger and 12 older adults during a speech perception task performed in both quiet and noisy listening conditions. Functional networks were constructed for each subject and listening condition based on inter-regional correlations of the fMRI signal among 66 cortical regions, and network measures of global and local efficiency were computed. Across listening conditions, older adult networks showed significantly decreased global (but not local) efficiency relative to younger adults after normalizing measures to surrogate random networks. Although listening condition produced no main effects on whole-cortex network organization, a significant age group x listening condition interaction was observed. Additionally, an exploratory analysis of regional effects uncovered age-related declines in both global and local efficiency concentrated exclusively in auditory areas (bilateral superior and middle temporal cortex), further suggestive of specificity to the speech perception tasks. Global efficiency also correlated positively with mean cortical thickness across all subjects, establishing gross cortical atrophy as a task-independent contributor to age-related differences in functional organization. Together, our findings provide evidence of age-related disruptions in cortical functional network organization during speech perception tasks, and suggest that although task-independent effects such as cortical atrophy clearly underlie age-related changes in cortical functional organization, age-related differences also demonstrate sensitivity to task domains.

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.