Development of the 'rich club' in brain connectivity networks from 438 adolescents & adults aged 12 to 30

The 'rich club' coefficient describes a phenomenon where a network's hubs (high-degree nodes) are on average more intensely interconnected than lower-degree nodes. Networks with rich clubs often have an efficient, higher-order organization, but we do not yet know how the rich club emerges in the living brain, or how it changes as our brain networks develop. Here we chart the developmental trajectory of the rich club in anatomical brain networks from 438 subjects aged 12-30. Cortical networks were constructed from 68×68 connectivity matrices of fiber density, using whole-brain tractography in 4-Tesla 105-gradient high angular resolution diffusion images (HARDI). The adult and younger cohorts had rich clubs that included different nodes; the rich club effect intensified with age. Rich-club organization is a sign of a network's efficiency and robustness. These concepts and findings may be advantageous for studying brain maturation and abnormal brain development.

Genetics of path lengths in brain connectivity networks: HARDI-based maps in 457 adults

Brain connectivity analyses are increasingly popular for investigating organization. Many connectivity measures including path lengths are generally defined as the number of nodes traversed to connect a node in a graph to the others. Despite its name, path length is purely topological, and does not take into account the physical length of the connections. The distance of the trajectory may also be highly relevant, but is typically overlooked in connectivity analyses. Here we combined genotyping, anatomical MRI and HARDI to understand how our genes influence the cortical connections, using whole-brain tractography. We defined a new measure, based on Dijkstra's algorithm, to compute path lengths for tracts connecting pairs of cortical regions. We compiled these measures into matrices where elements represent the physical distance traveled along tracts. We then analyzed a large cohort of healthy twins and show that our path length measure is reliable, heritable, and influenced even in young adults by the Alzheimer's risk gene, CLU.

Intracranial Volume Estimation and Graph Theoretical Analysis of Brain Functional Connectivity Networks

Understanding pathways of neurological disorders requires extensive research on both functional and structural characteristics of the brain. This dissertation introduced two interrelated research endeavors, describing (1) a novel integrated approach for constructing functional connectivity networks (FCNs) of brain using non-invasive scalp EEG recordings; and (2) a decision aid for estimating intracranial volume (ICV). The approach in (1) was developed to study the alterations of networks in patients with pediatric epilepsy. Results demonstrated the existence of statistically significant (p

Hierarchical topological network analysis of anatomical human brain connectivity and differences related to sex and kinship

Modern non-invasive brain imaging technologies, such as diffusion weighted magnetic resonance imaging (DWI), enable the mapping of neural fiber tracts in the white matter, providing a basis to reconstruct a detailed map of brain structural connectivity networks. Brain connectivity networks differ from random networks in their topology, which can be measured using small worldness, modularity, and high-degree nodes (hubs). Still, little is known about how individual differences in structural brain network properties relate to age, sex, or genetic differences. Recently, some groups have reported brain network biomarkers that enable differentiation among individuals, pairs of individuals, and groups of individuals. In addition to studying new topological features, here we provide a unifying general method to investigate topological brain networks and connectivity differences between individuals, pairs of individuals, and groups of individuals at several levels of the data hierarchy, while appropriately controlling false discovery rate (FDR) errors. We apply our new method to a large dataset of high quality brain connectivity networks obtained from High Angular Resolution Diffusion Imaging (HARDI) tractography in 303 young adult twins, siblings, and unrelated people. Our proposed approach can accurately classify brain connectivity networks based on sex (93% accuracy) and kinship (88.5% accuracy). We find statistically significant differences associated with sex and kinship both in the brain connectivity networks and in derived topological metrics, such as the clustering coefficient and the communicability matrix.

Changes in anatomical brain connectivity between ages 12 and 30: A HARDI study of 467 adolescents and adults

Graph theory can be applied to matrices that represent the brain's anatomical connections, to better understand global properties of anatomical networks, such as their clustering, efficiency and "small-world" topology. Network analysis is popular in adult studies of connectivity, but only one study - in just 30 subjects - has examined how network measures change as the brain develops over this period. Here we assessed the developmental trajectory of graph theory metrics of structural brain connectivity in a cross-sectional study of 467 subjects, aged 12 to 30. We computed network measures from 70×70 connectivity matrices of fiber density generated using whole-brain tractography in 4-Tesla 105-gradient high angular resolution diffusion images (HARDI). We assessed global efficiency and modularity, and both age and age 2 effects were identified. HARDI-based connectivity maps are sensitive to the remodeling and refinement of structural brain connections as the human brain develops.

Test-retest reliability of graph theory measures of structural brain connectivity

The human connectome has recently become a popular research topic in neuroscience, and many new algorithms have been applied to analyze brain networks. In particular, network topology measures from graph theory have been adapted to analyze network efficiency and 'small-world' properties. While there has been a surge in the number of papers examining connectivity through graph theory, questions remain about its test-retest reliability (TRT). In particular, the reproducibility of structural connectivity measures has not been assessed. We examined the TRT of global connectivity measures generated from graph theory analyses of 17 young adults who underwent two high-angular resolution diffusion (HARDI) scans approximately 3 months apart. Of the measures assessed, modularity had the highest TRT, and it was stable across a range of sparsities (a thresholding parameter used to define which network edges are retained). These reliability measures underline the need to develop network descriptors that are robust to acquisition parameters.

Investigating brain connectivity heritability in a twin study using diffusion imaging data

Heritability of brain anatomical connectivity has been studied with diffusion-weighted imaging (DWI) mainly by modeling each voxel's diffusion pattern as a tensor (e.g., to compute fractional anisotropy), but this method cannot accurately represent the many crossing connections present in the brain. We hypothesized that different brain networks (i.e., their component fibers) might have different heritability and we investigated brain connectivity using High Angular Resolution Diffusion Imaging (HARDI) in a cohort of twins comprising 328 subjects that included 70 pairs of monozygotic and 91 pairs of dizygotic twins. Water diffusion was modeled in each voxel with a Fiber Orientation Distribution (FOD) function to study heritability for multiple fiber orientations in each voxel. Precision was estimated in a test-retest experiment on a sub-cohort of 39 subjects. This was taken into account when computing heritability of FOD peaks using an ACE model on the monozygotic and dizygotic twins. Our results confirmed the overall heritability of the major white matter tracts but also identified differences in heritability between connectivity networks. Inter-hemispheric connections tended to be more heritable than intra-hemispheric and cortico-spinal connections. The highly heritable tracts were found to connect particular cortical regions, such as medial frontal cortices, postcentral, paracentral gyri, and the right hippocampus.

A Dynamic Directional Model for Effective Brain Connectivity using Electrocorticographic (ECoG) Time Series.

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.

Multiple Pathways Analysis of Brain Functional Networks from EEG Signals: An Application to Real Data

In the present study, we propose a theoretical graph procedure to investigate multiple pathways in brain functional networks. By taking into account all the possible paths consisting of h links between the nodes pairs of the network, we measured the global network redundancy R (h) as the number of parallel paths and the global network permeability P (h) as the probability to get connected. We used this procedure to investigate the structural and dynamical changes in the cortical networks estimated from a dataset of high-resolution EEG signals in a group of spinal cord injured (SCI) patients during the attempt of foot movement. In the light of a statistical contrast with a healthy population, the permeability index P (h) of the SCI networks increased significantly (P < 0.01) in the Theta frequency band (3-6 Hz) for distances h ranging from 2 to 4. On the contrary, no significant differences were found between the two populations for the redundancy index R (h) . The most significant changes in the brain functional network of SCI patients occurred mainly in the lower spectral contents. These changes were related to an improved propagation of communication between the closest cortical areas rather than to a different level of redundancy. This evidence strengthens the hypothesis of the need for a higher functional interaction among the closest ROIs as a mechanism to compensate the lack of feedback from the peripheral nerves to the sensomotor areas.

A graph-theoretical approach in brain functional networks. Possible implications in EEG studies

Abstract Background Recently, it was realized that the functional connectivity networks estimated from actual brain-imaging technologies (MEG, fMRI and EEG) can be analyzed by means of the graph theory, that is a mathematical representation of a network, which is essentially reduced to nodes and connections between them. Methods We used high-resolution EEG technology to enhance the poor spatial information of the EEG activity on the scalp and it gives a measure of the electrical activity on the cortical surface. Afterwards, we used the Directed Transfer Function (DTF) that is a multivariate spectral measure for the estimation of the directional influences between any given pair of channels in a multivariate dataset. Finally, a graph theoretical approach was used to model the brain networks as graphs. These methods were used to analyze the structure of cortical connectivity during the attempt to move a paralyzed limb in a group (N=5) of spinal cord injured patients and during the movement execution in a group (N=5) of healthy subjects. Results Analysis performed on the cortical networks estimated from the group of normal and SCI patients revealed that both groups present few nodes with a high out-degree value (i.e. outgoing links). This property is valid in the networks estimated for all the frequency bands investigated. In particular, cingulate motor areas (CMAs) ROIs act as ‘‘hubs’’ for the outflow of information in both groups, SCI and healthy. Results also suggest that spinal cord injuries affect the functional architecture of the cortical network sub-serving the volition of motor acts mainly in its local feature property. In particular, a higher local efficiency El can be observed in the SCI patients for three frequency bands, theta (3-6 Hz), alpha (7-12 Hz) and beta (13-29 Hz). By taking into account all the possible pathways between different ROI couples, we were able to separate clearly the network properties of the SCI group from the CTRL group. In particular, we report a sort of compensatory mechanism in the SCI patients for the Theta (3-6 Hz) frequency band, indicating a higher level of “activation” Ω within the cortical network during the motor task. The activation index is directly related to diffusion, a type of dynamics that underlies several biological systems including possible spreading of neuronal activation across several cortical regions. Conclusions The present study aims at demonstrating the possible applications of graph theoretical approaches in the analyses of brain functional connectivity from EEG signals. In particular, the methodological aspects of the i) cortical activity from scalp EEG signals, ii) functional connectivity estimations iii) graph theoretical indexes are emphasized in the present paper to show their impact in a real application.

Brain connectivity at different time-scales measured with EEG

We present an overview of different methods for decomposing a multichannel spontaneous electroencephalogram (EEG) into sets of temporal patterns and topographic distributions. All of the methods presented here consider the scalp electric field as the basic analysis entity in space. In time, the resolution of the methods is between milliseconds (time-domain analysis), subseconds (time- and frequency-domain analysis) and seconds (frequency-domain analysis). For any of these methods, we show that large parts of the data can be explained by a small number of topographic distributions. Physically, this implies that the brain regions that generated one of those topographies must have been active with a common phase. If several brain regions are producing EEG signals at the same time and frequency, they have a strong tendency to do this in a synchronized mode. This view is illustrated by several examples (including combined EEG and functional magnetic resonance imaging (fMRI)) and a selective review of the literature. The findings are discussed in terms of short-lasting binding between different brain regions through synchronized oscillations, which could constitute a mechanism to form transient, functional neurocognitive networks.

Linking brain connectivity across different time scales with electroencephalogram, functional magnetic resonance imaging, and diffusion tensor imaging

Structural and functional connectivity are intrinsic properties of the human brain and represent the amount of cognitive capacities of individual subjects. These connections are modulated due to development, learning, and disease. Momentary adaptations in functional connectivity alter the structural connections, which in turn affect the functional connectivity. Thus, structural and functional connectivity interact on a broad timescale. In this study, we aimed to explore distinct measures of connectivity assessed by functional magnetic resonance imaging and diffusion tensor imaging and their association to the dominant electroencephalogram oscillatory property at rest: the individual alpha frequency (IAF). We found that in 21 healthy young subjects, small intraindividual temporal IAF fluctuations were correlated to increased blood oxygenation level-dependent signal in brain areas associated to working memory functions and to the modulation of attention. These areas colocalized with functionally connected networks supporting the respective functions. Furthermore, subjects with higher IAF show increased fractional anisotropy values in fascicles connecting the above-mentioned areas and networks. Hence, due to a multimodal approach a consistent functionally and structurally connected network related to IAF was observed.

Repeatability analysis of global and local metrics of brain structural networks

Computational network analysis provides new methods to analyze the human connectome. Brain structural networks can be characterized by global and local metrics that recently gave promising insights for diagnosis and further understanding of neurological, psychiatric and neurodegenerative disorders. In order to ensure the validity of results in clinical settings the precision and repeatability of the networks and the associated metrics must be evaluated. In the present study, nineteen healthy subjects underwent two consecutive measurements enabling us to test reproducibility of the brain network and its global and local metrics. As it is known that the network topology depends on the network density, the effects of setting a common density threshold for all networks were also assessed. Results showed good to excellent repeatability for global metrics, while for local metrics it was more variable and some metrics were found to have locally poor repeatability. Moreover, between subjects differences were slightly inflated when the density was not fixed. At the global level, these findings confirm previous results on the validity of global network metrics as clinical biomarkers. However, the new results in our work indicate that the remaining variability at the local level as well as the effect of methodological characteristics on the network topology should be considered in the analysis of brain structural networks and especially in networks comparisons.

Validation of network communicability metrics for the analysis of brain structural networks.

Computational network analysis provides new methods to analyze the brain's structural organization based on diffusion imaging tractography data. Networks are characterized by global and local metrics that have recently given promising insights into diagnosis and the further understanding of psychiatric and neurologic disorders. Most of these metrics are based on the idea that information in a network flows along the shortest paths. In contrast to this notion, communicability is a broader measure of connectivity which assumes that information could flow along all possible paths between two nodes. In our work, the features of network metrics related to communicability were explored for the first time in the healthy structural brain network. In addition, the sensitivity of such metrics was analysed using simulated lesions to specific nodes and network connections. Results showed advantages of communicability over conventional metrics in detecting densely connected nodes as well as subsets of nodes vulnerable to lesions. In addition, communicability centrality was shown to be widely affected by the lesions and the changes were negatively correlated with the distance from lesion site. In summary, our analysis suggests that communicability metrics that may provide an insight into the integrative properties of the structural brain network and that these metrics may be useful for the analysis of brain networks in the presence of lesions. Nevertheless, the interpretation of communicability is not straightforward; hence these metrics should be used as a supplement to the more standard connectivity network metrics.