Small-world properties of nonlinear brain activity in schizophrenia

Graph-based network analysis in schizophrenia

Over the last few years, many studies have been published using modern network analysis of the brain. Researchers and practical doctors alike should understand this method and its results on the brain evaluation at rest, during activation and in brain disease. The studies are noninvasive and usually performed with elecroencephalographic, magnetoencephalographic, magnetic resonance imaging and diffusion tensor imaging brain recordings. Different tools for analysis have been developed, although the methods are in their early stages. The results of these analyses are of special value. Studies of these tools in schizophrenia are important because widespread and local network disturbances can be evaluated by assessing integration, segregation and several structural and functional properties. With the help of network analyses, the main findings in schizophrenia are lower optimum network organization, less efficiently wired networks, less local clustering, less hierarchical organization and signs of disconnection. There are only about twenty five relevant papers on the subject today. Only a few years of study of these methods have produced interesting results and it appears promising that the development of these methods will present important knowledge for both the preclinical signs of schizophrenia and the methods’ therapeutic effects.

A strong parietal hub in the small-world network of coloured-hearing synaesthetes during resting state EEG

We investigated whether functional brain networks are different in coloured-hearing synaesthetes compared with non-synaesthetes. Based on resting state electroencephalographic (EEG) activity, graph-theoretical analysis was applied to functional connectivity data obtained from different frequency bands (theta, alpha1, alpha2, and beta) of 12 coloured-hearing synaesthetes and 13 non-synaesthetes. The analysis of functional connectivity was based on estimated intra-cerebral sources of brain activation using standardized low-resolution electrical tomography. These intra-cerebral sources of brain activity were subjected to graph-theoretical analysis yielding measures representing small-world network characteristics (cluster coefficients and path length). In addition, brain regions with strong interconnections were identified (so-called hubs), and the interconnectedness of these hubs were quantified using degree as a measure of connectedness. Our analysis was guided by the two-stage model proposed by Hubbard and Ramachandran (2005). In this model, the parietal lobe is thought to play a pivotal role in binding together the synaesthetic perceptions (hyperbinding). In addition, we hypothesized that the auditory cortex and the fusiform gyrus would qualify as strong hubs in synaesthetes. Although synaesthetes and non-synaesthetes demonstrated a similar small-world network topology, the parietal lobe turned out to be a stronger hub in synaesthetes than in non-synaesthetes supporting the two-stage model. The auditory cortex was also identified as a strong hub in these coloured-hearing synaesthetes (for the alpha2 band). Thus, our a priori hypotheses receive strong support. Several additional hubs (for which no a priori hypothesis has been formulated) were found to be different in terms of the degree measure in synaesthetes, with synaesthetes demonstrating stronger degree measures indicating stronger interconnectedness. These hubs were found in brain areas known to be involved in controlling memory processes (alpha1: hippocampus and retrosplenial area), executive functions (alpha1 and alpha2: ventrolateral prefrontal cortex; theta: inferior frontal cortex), and the generation of perceptions (theta: extrastriate cortex; beta: subcentral area). Taken together this graph-theoretical analysis of the resting state EEG supports the two-stage model in demonstrating that the left-sided parietal lobe is a strong hub region, which is stronger functionally interconnected in synaesthetes than in non-synaesthetes. The right-sided auditory cortex is also a strong hub supporting the idea that coloured-hearing synaesthetes demonstrate a specific auditory cortex. A further important point is that these hub regions are even differently operating at rest supporting the idea that these hub characteristics are predetermining factors of coloured-hearing synaesthesia.

Clinical symptoms and alpha band resting-state functional connectivity imaging in patients with schizophrenia: implications for novel approaches to treatment

BACKGROUND

Schizophrenia (SZ) is associated with functional decoupling between cortical regions, but we do not know whether and where this occurs in low-frequency electromagnetic oscillations. The goal of this study was to use magnetoencephalography (MEG) to identify brain regions that exhibit abnormal resting-state connectivity in the alpha frequency range in patients with schizophrenia and investigate associations between functional connectivity and clinical symptoms in stable outpatient participants.

METHODS

Thirty patients with SZ and 15 healthy comparison participants were scanned in resting-state MEG (eyes closed). Functional connectivity MEG source data were reconstructed globally in the alpha range, quantified by the mean imaginary coherence between a voxel and the rest of the brain.

RESULTS

In patients, decreased connectivity was observed in left prefrontal cortex (PFC) and right superior temporal cortex, whereas increased connectivity was observed in left extrastriate cortex and the right inferior PFC. Functional connectivity of left inferior parietal cortex was negatively related to positive symptoms. Low left PFC connectivity was associated with negative symptoms. Functional connectivity of midline PFC was negatively correlated with depressed symptoms. Functional connectivity of right PFC was associated with other (cognitive) symptoms.

CONCLUSIONS

This study demonstrates direct functional disconnection in SZ between specific cortical fields within low-frequency resting-state oscillations. Impaired alpha coupling in frontal, parietal, and temporal regions is associated with clinical symptoms in these stable outpatients. Our findings indicate that this level of functional disconnection between cortical regions is an important treatment target in SZ.

Computational model prospective on the observation of proictal states in epileptic neuronal systems

Epilepsy is a pathological condition of the human central nervous system in which normal brain functions are impaired by unexpected transitions to states called seizures. We developed a lumped neuronal model that has the property of switching between two states as a result of intrinsic or extrinsic perturbations, such as noisy fluctuations. In one version of the model, seizure risk is controlled by a single connectivity parameter representing excitatory couplings between two model lumps. We show that this risk can be reconstructed from calculation of the cross-covariance between the activities of the two neural populations during the nonictal phase. In a second simulation sequence, we use a system of 10 interconnected lumps with randomly generated connectivity matrices. We show again that the tendency to develop seizures can be inferred from the cross-covariances calculated during the nonictal states. Our conclusion is that the risk of epileptic transitions in biological systems can be objectively quantified. This article is part of a Supplemental Special Issue entitled The Future of Automated Seizure Detection and Prediction.

How reliable are the functional connectivity networks of MEG in resting states?

We investigated the reliability of nodal network metrics of functional connectivity (FC) networks of magnetoencephalography (MEG) covering the whole brain at the sensor level in the eyes-closed (EC) and eyes-open (EO) resting states. Mutual information (MI) was employed as a measure of FC between sensors in theta, alpha, beta, and gamma frequency bands of MEG signals. MI matrices were assessed with three nodal network metrics, i.e., nodal degree (Dnodal), nodal efficiency (Enodal), and betweenness centrality (normBC). Intraclass correlation (ICC) values were calculated as a measure of reliability. We observed that the test-retest reliabilities of the resting states ranged from a poor to good level depending on the bands and metrics used for defining the nodal centrality. The dominant alpha-band FC network changes were the salient features of the state-related FC changes. The FC networks in the EO resting state showed greater reliability when assessed by Dnodal (maximum mean ICC = 0.655) and Enodal (maximum mean ICC = 0.604) metrics. The gamma-band FC network was less reliable than the theta, alpha, and beta networks across the nodal network metrics. However, the sensor-wise ICC values for the nodal centrality metrics were not uniformly distributed, that is, some sensors had high reliability. This study provides a sense of how the nodal centralities of the human resting state MEG are distributed at the sensor level and how reliable they are. It also provides a fundamental scientific background for continued examination of the resting state of human MEG.

Disrupted modular brain dynamics reflect cognitive dysfunction in Alzheimer's disease

The relation between pathology and cognitive dysfunction in dementia is still poorly understood, although disturbed communication between different brain regions is almost certainly involved. In this study we combine magneto-encephalography (MEG) and network analysis to investigate the role of functional sub-networks (modules) in the brain with regard to cognitive failure in Alzheimer's disease. Whole-head resting-state (MEG) was performed in 18 Alzheimer patients (age 67 ± 9, 6 females, MMSE 23 ± 5) and 18 healthy controls (age 66 ± 9, 11 females, MMSE 29 ± 1). We constructed functional brain networks based on interregional synchronization measurements, and performed graph theoretical analysis with a focus on modular organization. The overall modular strength and the number of modules changed significantly in Alzheimer patients. The parietal cortex was the most highly connected network area, but showed the strongest intramodular losses. Nonetheless, weakening of intermodular connectivity was even more outspoken, and more strongly related to cognitive impairment. The results of this study demonstrate that particularly the loss of communication between different functional brain regions reflects cognitive decline in Alzheimer's disease. These findings imply the relevance of regarding dementia as a functional network disorder.

Functional embedding predicts the variability of neural activity

Neural activity is irregular and unpredictable, yet little is known about why this is the case and how this property relates to the functional architecture of the brain. Here we show that the variability of a region’s activity systematically varies according to its topological role in functional networks. We recorded the resting-state electroencephalogram (EEG) and constructed undirected graphs of functional networks. We measured the centrality of each node in terms of the number of connections it makes (degree), the ease with which the node can be reached from other nodes in the network (efficiency) and the tendency of the node to occupy a position on the shortest paths between other pairs of nodes in the network (betweenness). As a proxy for variability, we estimated the information content of neural activity using multiscale entropy analysis. We found that the rate at which information was generated was largely predicted by centrality. Namely, nodes with greater degree, betweenness, and efficiency were more likely to have high information content, while peripheral nodes had relatively low information content. These results suggest that the variability of regional activity reflects functional embedding.

Does sleep restore the topology of functional brain networks?

Previous studies have shown that healthy anatomical as well as functional brain networks have small-world properties and become less optimal with brain disease. During sleep, the functional brain network becomes more small-world-like. Here we test the hypothesis that the functional brain network during wakefulness becomes less optimal after sleep deprivation (SD). Electroencephalography (EEG) was recorded five times a day after a night of SD and after a night of normal sleep in eight young healthy subjects, both during eyes-closed and eyes-open resting state. Overall synchronization was determined with the synchronization likelihood (SL) and the phase lag index (PLI). From these coupling strength matrices the normalized clustering coefficient C (a measurement of local clustering) and path length L (a measurement of global integration) were computed. Both measures were normalized by dividing them by their corresponding C-s and L-s values of random control networks. SD reduced alpha band C/C-s and L/L-s and theta band C/C-s during eyes-closed resting state. In contrast, SD increased gamma-band C/C-s and L/L-s during eyes-open resting state. Functional relevance of these changes in network properties was suggested by their association with sleep deprivation-induced performance deficits on a sustained attention simple reaction time task. The findings indicate that SD results in a more random network of alpha-coupling and a more ordered network of gamma-coupling. The present study shows that SD induces frequency-specific changes in the functional network topology of the brain, supporting the idea that sleep plays a role in the maintenance of an optimal functional network.

Altered resting state complexity in schizophrenia

The complexity of the human brain's activity and connectivity varies over temporal scales and is altered in disease states such as schizophrenia. Using a multi-level analysis of spontaneous low-frequency fMRI data stretching from the activity of individual brain regions to the coordinated connectivity pattern of the whole brain, we investigate the role of brain signal complexity in schizophrenia. Specifically, we quantitatively characterize the univariate wavelet entropy of regional activity, the bivariate pairwise functional connectivity between regions, and the multivariate network organization of connectivity patterns. Our results indicate that univariate measures of complexity are less sensitive to disease state than higher level bivariate and multivariate measures. While wavelet entropy is unaffected by disease state, the magnitude of pairwise functional connectivity is significantly decreased in schizophrenia and the variance is increased. Furthermore, by considering the network structure as a function of correlation strength, we find that network organization specifically of weak connections is strongly correlated with attention, memory, and negative symptom scores and displays potential as a clinical biomarker, providing up to 75% classification accuracy and 85% sensitivity. We also develop a general statistical framework for the testing of group differences in network properties, which is broadly applicable to studies where changes in network organization are crucial to the understanding of brain function.

Optimization of seed density in DTI tractography for structural networks

Diffusion tensor imaging (DTI) has been used for mapping the structural network of the human brain. The network can be constructed by choosing various brain regions as nodes and fiber tracts connecting those regions as links. The structural network generated from DTI data can be affected by noise in the scans and the choice of tractography algorithm. This study aimed to examine the effect of the number of seeds in tractography on the variance of structural networks. The variance of the network was characterized using an approach similar to the National Electrical Manufacturers Association (NEMA) standards for measurement of image noise. It was shown that the variance of the network is inversely related to the square root of seed density. Consequently, the number of seeds has a large impact on local characteristics and metrics of the network architecture. As the number of seeds increased, increased stability of structural network metrics was observed. However, more seeds can also lead to more spurious fibers and thus affect nodal degrees and edge weights, and proper thresholding may be necessary to create an appropriate weighted network. Because the variance of the network is also influenced by other imaging factors, further increase in the number of seeds has little effect in reducing the network variance. The selection of the seed number should be a balance between the network variance and computational effort.

Altered topological properties of functional network connectivity in schizophrenia during resting state: a small-world brain network study

Aberrant topological properties of small-world human brain networks in patients with schizophrenia (SZ) have been documented in previous neuroimaging studies. Aberrant functional network connectivity (FNC, temporal relationships among independent component time courses) has also been found in SZ by a previous resting state functional magnetic resonance imaging (fMRI) study. However, no study has yet determined if topological properties of FNC are also altered in SZ. In this study, small-world network metrics of FNC during the resting state were examined in both healthy controls (HCs) and SZ subjects. FMRI data were obtained from 19 HCs and 19 SZ. Brain images were decomposed into independent components (ICs) by group independent component analysis (ICA). FNC maps were constructed via a partial correlation analysis of ICA time courses. A set of undirected graphs were built by thresholding the FNC maps and the small-world network metrics of these maps were evaluated. Our results demonstrated significantly altered topological properties of FNC in SZ relative to controls. In addition, topological measures of many ICs involving frontal, parietal, occipital and cerebellar areas were altered in SZ relative to controls. Specifically, topological measures of whole network and specific components in SZ were correlated with scores on the negative symptom scale of the Positive and Negative Symptom Scale (PANSS). These findings suggest that aberrant architecture of small-world brain topology in SZ consists of ICA temporally coherent brain networks.

Anatomical insights into disrupted small-world networks in schizophrenia

Schizophrenia is characterized by lowered efficiency in distributed information processing, as indicated by research that identified a disrupted small-world functional network. However, whether the dysconnection manifested by the disrupted small-world functional network is reflected in underlying anatomical disruption in schizophrenia remains unresolved. This study examined the topological properties of human brain anatomical networks derived from diffusion tensor imaging in patients with schizophrenia and in healthy controls. We constructed the weighted brain anatomical network for each of 79 schizophrenia patients and for 96 age and gender matched healthy subjects using diffusion tensor tractography and calculated the topological properties of the networks using a graph theoretical method. The topological properties of the patients' anatomical networks were altered, in that global efficiency decreased but local efficiency remained unchanged. The deleterious effects of schizophrenia on network performance appear to be localized as reduced regional efficiency in hubs such as the frontal associative cortices, the paralimbic/limbic regions and a subcortical structure (the left putamen). Additionally, scores on the Positive and Negative Symptom Scale correlated negatively with efficient network properties in schizophrenia. These findings suggest that complex brain network analysis may potentially be used to detect an imaging biomarker for schizophrenia.

The relationship between regional and inter-regional functional connectivity deficits in schizophrenia

While schizophrenia is frequently characterized as a disorder of disturbed functional connectivity, the causes and pathophysiological origins of such disturbances remain unclear. The aim of this study was to better elucidate the mechanistic causes of abnormal functional connectivity in schizophrenia, measured as the extent of temporal correlation between endogenous fluctuations recorded at anatomically discrete brain regions during resting-state functional MRI. An approach was developed to perform whole-brain connectivity mapping at the resolution of individual pairs of voxels, without the need for arbitrary parcellation of the cerebrum. Between-group connectivity reductions in 12 people diagnosed with schizophrenia and 15 age-, IQ-, and gender-matched healthy volunteers were localized to a distributed network including frontoparietal and occipitoparietal connections. The gray-matter regions comprising this disturbed network showed evidence of local reductions in both intra-regional homogeneity (29%-33% reduction) and signal power (40%-60% reduction). The extent to which inter-regional correlation was reduced between a pair of gray matter regions was found to be strongly correlated with the extent of local decoherence evident within the gray matter regions per se. This suggests measurement of aberrant functional connectivity in schizophrenia is both a measurement of altered coupling between regions as well as a measurement of local decoherence within regions.

Failure tolerance of spike phase synchronization in coupled neural networks

Neuronal synchronization plays an important role in the various functionality of nervous system such as binding, cognition, information processing, and computation. In this paper, we investigated how random and intentional failures in the nodes of a network influence its phase synchronization properties. We considered both artificially constructed networks using models such as preferential attachment, Watts-Strogatz, and Erdős-Rényi as well as a number of real neuronal networks. The failure strategy was either random or intentional based on properties of the nodes such as degree, clustering coefficient, betweenness centrality, and vulnerability. Hindmarsh-Rose model was considered as the mathematical model for the individual neurons, and the phase synchronization of the spike trains was monitored as a function of the percentage∕number of removed nodes. The numerical simulations were supplemented by considering coupled non-identical Kuramoto oscillators. Failures based on the clustering coefficient, i.e., removing the nodes with high values of the clustering coefficient, had the least effect on the spike synchrony in all of the networks. This was followed by errors where the nodes were removed randomly. However, the behavior of the other three attack strategies was not uniform across the networks, and different strategies were the most influential in different network structure.

Integrative etiopathogenetic models of psychotic disorders: methods, evidence and concepts

Integrative models of the etiopathogesnesis of psychotic disorders are needed since a wealth of information from such diverse fields as neurobiology, psychology, and the social sciences is currently changing the concepts of mental disorders. Several approaches to integrate these streams of information into coherent concepts of psychosis are feasible and will need to be assessed in future experimental studies. Common to these concepts are the notion of psychotic disorders as brain disorders and a polythetic approach in that it is increasingly realized that a multitude of interindividually partially different pathogenetic factors interact in individual persons in a complex fashion resulting in the clinical symptoms of psychosis.

Test-retest reliability of resting-state connectivity network characteristics using fMRI and graph theoretical measures

Characterizing the brain connectome using neuroimaging data and measures derived from graph theory emerged as a new approach that has been applied to brain maturation, cognitive function and neuropsychiatric disorders. For a broad application of this method especially for clinical populations and longitudinal studies, the reliability of this approach and its robustness to confounding factors need to be explored. Here we investigated test-retest reliability of graph metrics of functional networks derived from functional magnetic resonance imaging (fMRI) recorded in 33 healthy subjects during rest. We constructed undirected networks based on the Anatomic-Automatic-Labeling (AAL) atlas template and calculated several commonly used measures from the field of graph theory, focusing on the influence of different strategies for confound correction. For each subject, method and session we computed the following graph metrics: clustering coefficient, characteristic path length, local and global efficiency, assortativity, modularity, hierarchy and the small-worldness scalar. Reliability of each graph metric was assessed using the intraclass correlation coefficient (ICC). Overall ICCs ranged from low to high (0 to 0.763) depending on the method and metric. Methodologically, the use of a broader frequency band (0.008-0.15 Hz) yielded highest reliability indices (mean ICC=0.484), followed by the use of global regression (mean ICC=0.399). In general, the second order metrics (small-worldness, hierarchy, assortativity) studied here, tended to be more robust than first order metrics. In conclusion, our study provides methodological recommendations which allow the computation of sufficiently robust markers of network organization using graph metrics derived from fMRI data at rest.

Constrained randomization of weighted networks

We propose a Markov chain method to efficiently generate surrogate networks that are random under the constraint of given vertex strengths. With these strength-preserving surrogates and with edge-weight-preserving surrogates we investigate the clustering coefficient and the average shortest path length of functional networks of the human brain as well as of the International Trade Networks. We demonstrate that surrogate networks can provide additional information about network-specific characteristics and thus help interpreting empirical weighted networks.

Brain graphs: graphical models of the human brain connectome

Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptual review and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

On the Influence of Amplitude on the Connectivity between Phases

In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with "no": for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the "real" underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson-Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson-Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators' amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large.

General and specific functional connectivity disturbances in first-episode schizophrenia during cognitive control performance

BACKGROUND

Cognitive control impairments in schizophrenia are thought to arise from dysfunction of interconnected networks of brain regions, but interrogating the functional dynamics of large-scale brain networks during cognitive task performance has proved difficult. We used functional magnetic resonance imaging to generate event-related whole-brain functional connectivity networks in participants with first-episode schizophrenia and healthy control subjects performing a cognitive control task.

METHODS

Functional connectivity during cognitive control performance was assessed between each pair of 78 brain regions in 23 patients and 25 control subjects. Network properties examined were region-wise connectivity, edge-wise connectivity, global path length, clustering, small-worldness, global efficiency, and local efficiency.

RESULTS

Patients showed widespread functional connectivity deficits in a large-scale network of brain regions, which primarily affected connectivity between frontal cortex and posterior regions and occurred irrespective of task context. A more circumscribed and task-specific connectivity impairment in frontoparietal systems related to cognitive control was also apparent. Global properties of network topology in patients were relatively intact.

CONCLUSIONS

The first episode of schizophrenia is associated with a generalized connectivity impairment affecting most brain regions but that is particularly pronounced for frontal cortex. Superimposed on this generalized deficit, patients show more specific cognitive-control-related functional connectivity reductions in frontoparietal regions. These connectivity deficits occur in the context of relatively preserved global network organization.

Automated discrimination of brain pathological state attending to complex structural brain network properties: the shiverer mutant mouse case

Neuroimaging classification procedures between normal and pathological subjects are sparse and highly dependent of an expert's clinical criterion. Here, we aimed to investigate whether possible brain structural network differences in the shiverer mouse mutant, a relevant animal model of myelin related diseases, can reflect intrinsic individual brain properties that allow the automatic discrimination between the shiverer and normal subjects. Common structural networks properties between shiverer (C3Fe.SWV Mbp(shi)/Mbp(shi), n = 6) and background control (C3HeB.FeJ, n = 6) mice are estimated and compared by means of three diffusion weighted MRI (DW-MRI) fiber tractography algorithms and a graph framework. Firstly, we found that brain networks of control group are significantly more clustered, modularized, efficient and optimized than those of the shiverer group, which presented significantly increased characteristic path length. These results are in line with previous structural/functional complex brain networks analysis that have revealed topologic differences and brain network randomization associated to specific states of human brain pathology. In addition, by means of network measures spatial representations and discrimination analysis, we show that it is possible to classify with high accuracy to which group each subject belongs, providing also a probability value of being a normal or shiverer subject as an individual anatomical classifier. The obtained correct predictions (e.g., around 91.6-100%) and clear spatial subdivisions between control and shiverer mice, suggest that there might exist specific network subspaces corresponding to specific brain disorders, supporting also the point of view that complex brain network analyses constitutes promising tools in the future creation of interpretable imaging biomarkers.

Exponential random graph modeling for complex brain networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks.

Functional brain network efficiency predicts intelligence

The neuronal causes of individual differences in mental abilities such as intelligence are complex and profoundly important. Understanding these abilities has the potential to facilitate their enhancement. The purpose of this study was to identify the functional brain network characteristics and their relation to psychometric intelligence. In particular, we examined whether the functional network exhibits efficient small-world network attributes (high clustering and short path length) and whether these small-world network parameters are associated with intellectual performance. High-density resting state electroencephalography (EEG) was recorded in 74 healthy subjects to analyze graph-theoretical functional network characteristics at an intracortical level. Ravens advanced progressive matrices were used to assess intelligence. We found that the clustering coefficient and path length of the functional network are strongly related to intelligence. Thus, the more intelligent the subjects are the more the functional brain network resembles a small-world network. We further identified the parietal cortex as a main hub of this resting state network as indicated by increased degree centrality that is associated with higher intelligence. Taken together, this is the first study that substantiates the neural efficiency hypothesis as well as the Parieto-Frontal Integration Theory (P-FIT) of intelligence in the context of functional brain network characteristics. These theories are currently the most established intelligence theories in neuroscience. Our findings revealed robust evidence of an efficiently organized resting state functional brain network for highly productive cognitions.

Structural brain networks and neuropsychiatric disorders

PURPOSE OF REVIEW

Graph theoretical analysis of neuroimaging data has emerged in the last few years as a powerful yet accessible tool to examine brain connectivity in a quantitative framework. In this review, we summarize recent advances in structural brain network research pertaining to neuropsychiatric disorders.

RECENT FINDINGS

Although many neuropsychiatric disorder studies have used brain network approaches, the majority are of functional brain networks. However, seven recent studies, three on Alzheimer's disease, three on schizophrenia, and one on epilepsy, have used a structural brain network approach using either inter-regional cortical thickness, gray matter volume correlations, or diffusion tensor imaging tractography. The findings of these studies demonstrate that the structural brain network approach can be effectively used in the neuropsychiatric disorder studies to capture the abnormalities of regional and whole-brain network organizations.

SUMMARY

By modeling the brain as a complex network, we can use graph theoretical analysis to study neuropsychiatric disorders by exploring its topological attributes. The interesting findings of the limited number of previous studies from the perspective of brain connectivity should attract more researchers to apply this method. This emerging quantitative framework may lead us to better understanding of neuropsychiatric disorders.

Space-time network connectivity and cortical activations preceding spike wave discharges in human absence epilepsy: a MEG study

To describe the spatial and temporal profiles of connectivity networks and sources preceding generalized spike-and-wave discharges (SWDs) in human absence epilepsy. Nonlinear associations of MEG signals and cluster indices obtained within the framework of graph theory were determined, while source localization in the frequency domain was performed in the low frequency bands with dynamic imaging of coherent sources. The results were projected on a three-dimensional surface rendering of the brain using a semi-realistic head model and MRI images obtained for each of the five patients studied. An increase in clustering and a decrease in path length preceding SWD onset and a rhythmic pattern of increasing and decreasing connectivity were seen during SWDs. Beamforming showed a consistent appearance of a low frequency frontal cortical source prior to the first generalized spikes. This source was preceded by a low frequency occipital source. The changes in the connectivity networks with the onset of SWDs suggest a pathologically predisposed state towards synchronous seizure networks with increasing connectivity from interictal to preictal and ictal state, while the occipital and frontal low frequency early preictal sources demonstrate that SWDs are not suddenly arising but gradually build up in a dynamic network.

Discrete neuroanatomical networks are associated with specific cognitive abilities in old age

There have been many attempts at explaining age-related cognitive decline on the basis of regional brain changes, with the usual but inconsistent findings being that smaller gray matter volumes in certain brain regions predict worse cognitive performance in specific domains. Additionally, compromised white matter integrity, as suggested by white matter hyperintensities or decreased regional white matter fractional anisotropy, has an adverse impact on cognitive functions. The human brain is, however, a network and it may be more appropriate to relate cognitive functions to properties of the network rather than specific brain regions. We report on graph theory-based analyses of diffusion tensor imaging tract-derived connectivity in a sample of 342 healthy individuals aged 72-92 years. The cognitive domains included processing speed, memory, language, visuospatial, and executive functions. We examined the association of these cognitive assessments with both the connectivity of the whole brain network and individual cortical regions. We found that the efficiency of the whole brain network of cortical fiber connections had an influence on processing speed and visuospatial and executive functions. Correlations between connectivity of specific regions and cognitive assessments were also observed, e.g., stronger connectivity in regions such as superior frontal gyrus and posterior cingulate cortex were associated with better executive function. Similar to the relationship between regional connectivity efficiency and age, greater processing speed was significantly correlated with better connectivity of nearly all the cortical regions. For the first time, regional anatomical connectivity maps related to processing speed and visuospatial and executive functions in the elderly are identified.

Disruption of functional connectivity of the default-mode network in alcoholism

The default mode network (DMN) comprises brain structures maximally active at rest. Disturbance of network nodes or their connections occurs with some neuropsychiatric conditions and may underlie associated dysfunction. DMN connectivity has not been examined in alcoholism, which is marked by compromised DMN nodes and impaired spatial working memory. To test whether performance would be related to DMN integrity, we examined DMN functional connectivity using functional magnetic resonance imaging (fMRI) data and graph theory analysis. We assumed that disruption of short paths between network nodes would attenuate processing efficiency. Alcoholics and controls were scanned at rest and during a spatial working memory task. At rest, the spontaneous slow fluctuations of fMRI signals in the posterior cingulate and cerebellar regions in alcoholics were less synchronized than in controls, indicative of compromised functional connectivity. Graph theory analysis indicated that during rest, alcoholics had significantly lower efficiency indices than controls between the posterior cingulate seed and multiple cerebellar sites. Greater efficiency in several connections correlated with longer sobriety in alcoholics. During the task, on which alcoholics performed on par with controls, connectivity between the left posterior cingulate seed and left cerebellar regions was more robust in alcoholics than controls and suggests compensatory networking to achieve normal performance.

Graph theoretical modeling of brain connectivity

PURPOSE OF REVIEW

In recent years, there has been an explosion of studies on network modeling of brain connectivity. This review will focus mainly on recent findings concerning graph theoretical analysis of human brain networks with a variety of imaging modalities, including structural MRI, diffusion MRI, functional MRI, and EEG/MEG.

RECENT FINDINGS

Recent studies have utilized graph theoretical approaches to investigate the organizational principles of brain networks. These studies have consistently shown many important statistical properties underlying the topological organization of the human brain, including modularity, small-worldness, and the existence of highly connected network hubs. Importantly, these quantifiable network properties were found to change during normal development, aging, and various neurological and neuropsychiatric diseases such as Alzheimer's disease and schizophrenia. Moreover, several studies have also suggested that these network properties correlate with behavioral and genetic factors.

SUMMARY

The exciting research regarding graph theoretical analysis of brain connectivity yields truly integrative and comprehensive descriptions of the structural and functional organization of the human brain, which provides important implications for health and disease. Future research will most likely involve integrative models of brain structural and functional connectivity with multimodal neuroimaging data, exploring whether graph-based brain network analysis could yield reliable biomarkers for disease diagnosis and treatment.

The non-random brain: efficiency, economy, and complex dynamics

Modern anatomical tracing and imaging techniques are beginning to reveal the structural anatomy of neural circuits at small and large scales in unprecedented detail. When examined with analytic tools from graph theory and network science, neural connectivity exhibits highly non-random features, including high clustering and short path length, as well as modules and highly central hub nodes. These characteristic topological features of neural connections shape non-random dynamic interactions that occur during spontaneous activity or in response to external stimulation. Disturbances of connectivity and thus of neural dynamics are thought to underlie a number of disease states of the brain, and some evidence suggests that degraded functional performance of brain networks may be the outcome of a process of randomization affecting their nodes and edges. This article provides a survey of the non-random structure of neural connectivity, primarily at the large scale of regions and pathways in the mammalian cerebral cortex. In addition, we will discuss how non-random connections can give rise to differentiated and complex patterns of dynamics and information flow. Finally, we will explore the idea that at least some disorders of the nervous system are associated with increased randomness of neural connections.

Graphic patterns of cortical functional connectivity of depressed patients on the basis of EEG measurements

Considerable evidences have shown a decrease of neuronal activity in the left frontal lobe of depressed patients, but the underlying cortical network is still unclear. The present study intends to investigate the conscious-state brain network patterns in depressed patients compared with control individuals. Cortical functional connectivity is quantified by the partial directed coherence (PDC) analysis of multichannel EEG signals from 12 depressed patients and 12 healthy volunteers. The corresponding PDC matrices are first converted into unweighted graphs by applying a threshold to obtain the topographic property in-degree (K(in)). A significantly larger K(in) in the left hemisphere is identified in depressed patients, while a symmetric pattern is found in the control group. Another two topographic measures, i.e., clustering coefficients (C) and characteristic path length (L), are obtained from the original weighted PDC digraphs. Compared with control individuals, significantly smaller C and L are revealed in the depression group, indicating a random network-like architecture due to affective disorder. This study thereby provides further support for the presence of a hemispheric asymmetry syndrome in the depressed patients. More importantly, we present evidence that depression is characterized by a loss of optimal small-world network characteristics in conscious state.

Disrupted axonal fiber connectivity in schizophrenia

BACKGROUND

Schizophrenia is believed to result from abnormal functional integration of neural processes thought to arise from aberrant brain connectivity. However, evidence for anatomical dysconnectivity has been equivocal, and few studies have examined axonal fiber connectivity in schizophrenia at the level of whole-brain networks.

METHODS

Cortico-cortical anatomical connectivity at the scale of axonal fiber bundles was modeled as a network. Eighty-two network nodes demarcated functionally specific cortical regions. Sixty-four direction diffusion tensor-imaging coupled with whole-brain tractography was performed to map the architecture via which network nodes were interconnected in each of 74 patients with schizophrenia and 32 age- and gender-matched control subjects. Testing was performed to identify pairs of nodes between which connectivity was impaired in the patient group. The connectional architecture of patients was tested for changes in five network attributes: nodal degree, small-worldness, efficiency, path length, and clustering.

RESULTS

Impaired connectivity in the patient group was found to involve a distributed network of nodes comprising medial frontal, parietal/occipital, and the left temporal lobe. Although small-world attributes were conserved in schizophrenia, the cortex was interconnected more sparsely and up to 20% less efficiently in patients. Intellectual performance was found to be associated with brain efficiency in control subjects but not in patients.

CONCLUSIONS

This study presents evidence of widespread dysconnectivity in white-matter connectional architecture in a large sample of patients with schizophrenia. When considered from the perspective of recent evidence for impaired synaptic plasticity, this study points to a multifaceted pathophysiology in schizophrenia encompassing axonal as well as putative synaptic mechanisms.

A shift to randomness of brain oscillations in people with autism

BACKGROUND

Resting-state functional magnetic resonance imaging (fMRI) enables investigation of the intrinsic functional organization of the brain. Fractal parameters such as the Hurst exponent, H, describe the complexity of endogenous low-frequency fMRI time series on a continuum from random (H = .5) to ordered (H = 1). Shifts in fractal scaling of physiological time series have been associated with neurological and cardiac conditions.

METHODS

Resting-state fMRI time series were recorded in 30 male adults with an autism spectrum condition (ASC) and 33 age- and IQ-matched male volunteers. The Hurst exponent was estimated in the wavelet domain and between-group differences were investigated at global and voxel level and in regions known to be involved in autism.

RESULTS

Complex fractal scaling of fMRI time series was found in both groups but globally there was a significant shift to randomness in the ASC (mean H = .758, SD = .045) compared with neurotypical volunteers (mean H = .788, SD = .047). Between-group differences in H, which was always reduced in the ASC group, were seen in most regions previously reported to be involved in autism, including cortical midline structures, medial temporal structures, lateral temporal and parietal structures, insula, amygdala, basal ganglia, thalamus, and inferior frontal gyrus. Severity of autistic symptoms was negatively correlated with H in retrosplenial and right anterior insular cortex.

CONCLUSIONS

Autism is associated with a small but significant shift to randomness of endogenous brain oscillations. Complexity measures may provide physiological indicators for autism as they have done for other medical conditions.

Statistical parametric network analysis of functional connectivity dynamics during a working memory task

Network analysis has become a tool of choice for the study of functional and structural Magnetic Resonance Imaging (MRI) data. Little research, however, has investigated connectivity dynamics in relation to varying cognitive load. In fMRI, correlations among slow (<0.1 Hz) fluctuations of blood oxygen level dependent (BOLD) signal can be used to construct functional connectivity networks. Using an anatomical parcellation scheme, we produced undirected weighted graphs linking 90 regions of the brain representing major cortical gyri and subcortical nuclei, in a population of healthy adults (n=43). Topological changes in these networks were investigated under different conditions of a classical working memory task - the N-back paradigm. A mass-univariate approach was adopted to construct statistical parametric networks (SPNs) that reflect significant modifications in functional connectivity between N-back conditions. Our proposed method allowed the extraction of 'lost' and 'gained' functional networks, providing concise graphical summaries of whole-brain network topological changes. Robust estimates of functional networks are obtained by pooling information about edges and vertices over subjects. Graph thresholding is therefore here supplanted by inference. The analysis proceeds by firstly considering changes in weighted cost (i.e. mean between-region correlation) over the different N-back conditions and secondly comparing small-world topological measures integrated over network cost, thereby controlling for differences in mean correlation between conditions. The results are threefold: (i) functional networks in the four conditions were all found to satisfy the small-world property and cost-integrated global and local efficiency levels were approximately preserved across the different experimental conditions; (ii) weighted cost considerably decreased as working memory load increased; and (iii) subject-specific weighted costs significantly predicted behavioral performances on the N-back task (Wald F=13.39,df(1)=1,df(2)=83,p<0.001), and therefore conferred predictive validity to functional connectivity strength, as measured by weighted cost. The results were found to be highly sensitive to the frequency band used for the computation of the between-region correlations, with the relationship between weighted cost and behavioral performance being most salient at very low frequencies (0.01-0.03 Hz). These findings are discussed in relation to the integration/specialization functional dichotomy. The pruning of functional networks under increasing cognitive load may permit greater modular specialization, thereby enhancing performance.

Comparing brain networks of different size and connectivity density using graph theory

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others.

Disrupted modularity and local connectivity of brain functional networks in childhood-onset schizophrenia

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.

Comorbidity: a network perspective

The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy.

Impaired efficiency of functional networks underlying episodic memory-for-context in schizophrenia

Memory for context and episodic memory have been identified as primary contributors to cognitive impairments in schizophrenia. This study examined neural networks involved in episodic memory-for-context in schizophrenia using a multimodal strategy including a graph theoretical approach, combined with an assessment of the contribution of structural impairments to disruption in the efficiency of functional brain networks. Twenty-three patients with schizophrenia and 33 healthy controls performed an episodic memory-for-context task while undergoing functional magnetic resonance imaging scanning. Graph theory was used to characterize the small-world properties of functional connections between activated regions, and a morphometric analysis was used to investigate schizophrenia-related structural deficits. Similar functional activations were identified in the two groups; however, although small-world properties were present in the topological organization of the functional networks in both groups, significant reductions in local, but not global, efficiency were observed in the schizophrenia group. Several key network "hub" regions related to recollection, such as the bilateral dorsal anterior cingulate gyrus, showed reduced gray matter volume in schizophrenia patients. These findings suggest that loss of gray matter volume may contribute to local inefficiencies in the architecture of the network underlying memory-for-context in schizophrenia.

Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity

The human brain undertakes highly sophisticated information processing facilitated by the interaction between its sub-regions. We present a novel method for interregional connectivity analysis, using multivariate extensions to the mutual information and transfer entropy. The method allows us to identify the underlying directed information structure between brain regions, and how that structure changes according to behavioral conditions. This method is distinguished in using asymmetric, multivariate, information-theoretical analysis, which captures not only directional and non-linear relationships, but also collective interactions. Importantly, the method is able to estimate multivariate information measures with only relatively little data. We demonstrate the method to analyze functional magnetic resonance imaging time series to establish the directed information structure between brain regions involved in a visuo-motor tracking task. Importantly, this results in a tiered structure, with known movement planning regions driving visual and motor control regions. Also, we examine the changes in this structure as the difficulty of the tracking task is increased. We find that task difficulty modulates the coupling strength between regions of a cortical network involved in movement planning and between motor cortex and the cerebellum which is involved in the fine-tuning of motor control. It is likely these methods will find utility in identifying interregional structure (and experimentally induced changes in this structure) in other cognitive tasks and data modalities.

Neurophysiological and computational principles of cortical rhythms in cognition

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

Spontaneous brain activity observed with functional magnetic resonance imaging as a potential biomarker in neuropsychiatric disorders

As functional magnetic resonance imaging (fMRI) studies have yielded increasing amounts of information about the brain's spontaneous activity, they have revealed fMRI's potential to locate changes in brain hemodynamics that are associated with neuropsychiatric disorders. In this paper, we review studies that support the notion that changes in brain spontaneous activity observed by fMRI can be used as potential biomarkers for diagnosis and treatment evaluation in neuropsychiatric disorders. We first review the methods used to study spontaneous activity from the perspectives of (1) the properties of local spontaneous activity, (2) the spatial pattern of spontaneous activity, and (3) the topological properties of brain networks. We also summarize the major findings associated with major neuropsychiatric disorders obtained using these methods. Then we review the pilot studies that have used spontaneous activity to discriminate patients from normal controls. Finally, we discuss current challenges and potential research directions to further elucidate the clinical use of spontaneous brain activity in neuropsychiatric disorders.

Functional connectivity and brain networks in schizophrenia

Schizophrenia has often been conceived as a disorder of connectivity between components of large-scale brain networks. We tested this hypothesis by measuring aspects of both functional connectivity and functional network topology derived from resting-state fMRI time series acquired at 72 cerebral regions over 17 min from 15 healthy volunteers (14 male, 1 female) and 12 people diagnosed with schizophrenia (10 male, 2 female). We investigated between-group differences in strength and diversity of functional connectivity in the 0.06-0.125 Hz frequency interval, and some topological properties of undirected graphs constructed from thresholded interregional correlation matrices. In people with schizophrenia, strength of functional connectivity was significantly decreased, whereas diversity of functional connections was increased. Topologically, functional brain networks had reduced clustering and small-worldness, reduced probability of high-degree hubs, and increased robustness in the schizophrenic group. Reduced degree and clustering were locally significant in medial parietal, premotor and cingulate, and right orbitofrontal cortical nodes of functional networks in schizophrenia. Functional connectivity and topological metrics were correlated with each other and with behavioral performance on a verbal fluency task. We conclude that people with schizophrenia tend to have a less strongly integrated, more diverse profile of brain functional connectivity, associated with a less hub-dominated configuration of complex brain functional networks. Alongside these behaviorally disadvantageous differences, however, brain networks in the schizophrenic group also showed a greater robustness to random attack, pointing to a possible benefit of the schizophrenia connectome, if less extremely expressed.

Using network science to evaluate exercise-associated brain changes in older adults

Literature has shown that exercise is beneficial for cognitive function in older adults and that aerobic fitness is associated with increased hippocampal tissue and blood volumes. The current study used novel network science methods to shed light on the neurophysiological implications of exercise-induced changes in the hippocampus of older adults. Participants represented a volunteer subgroup of older adults that were part of either the exercise training (ET) or healthy aging educational control (HAC) treatment arms from the Seniors Health and Activity Research Program Pilot (SHARP-P) trial. Following the 4-month interventions, MRI measures of resting brain blood flow and connectivity were performed. The ET group's hippocampal cerebral blood flow (CBF) exhibited statistically significant increases compared to the HAC group. Novel whole-brain network connectivity analyses showed greater connectivity in the hippocampi of the ET participants compared to HAC. Furthermore, the hippocampus was consistently shown to be within the same network neighborhood (module) as the anterior cingulate cortex only within the ET group. Thus, within the ET group, the hippocampus and anterior cingulate were highly interconnected and localized to the same network neighborhood. This project shows the power of network science to investigate potential mechanisms for exercise-induced benefits to the brain in older adults. We show a link between neurological network features and CBF, and it is possible that this alteration of functional brain networks may lead to the known improvement in cognitive function among older adults following exercise.

Graph theoretical analysis of structural and functional connectivity MRI in normal and pathological brain networks

Graph theoretical analysis of structural and functional connectivity MRI data (ie. diffusion tractography or cortical volume correlation and resting-state or task-related (effective) fMRI, respectively) has provided new measures of human brain organization in vivo. The most striking discovery is that the whole-brain network exhibits "small-world" properties shared with many other complex systems (social, technological, information, biological). This topology allows a high efficiency at different spatial and temporal scale with a very low wiring and energy cost. Its modular organization also allows for a high level of adaptation. In addition, degree distribution of brain networks demonstrates highly connected hubs that are crucial for the whole-network functioning. Many of these hubs have been identified in regions previously defined as belonging to the default-mode network (potentially explaining the high basal metabolism of this network) and the attentional networks. This could explain the crucial role of these hub regions in physiology (task-related fMRI data) as well as in pathophysiology. Indeed, such topological definition provides a reliable framework for predicting behavioral consequences of focal or multifocal lesions such as stroke, tumors or multiple sclerosis. It also brings new insights into a better understanding of pathophysiology of many neurological or psychiatric diseases affecting specific local or global brain networks such as epilepsy, Alzheimer's disease or schizophrenia. Graph theoretical analysis of connectivity MRI data provides an outstanding framework to merge anatomical and functional data in order to better understand brain pathologies.