Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions using functional multilayer networks whose layers represent the different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as a multilayer network in which all brain regions can interact with each other at different frequency bands, instead of as a multiplex network, in which interactions between different frequency bands are only allowed within each brain region and not between them. We study the second smallest eigenvalue of the combinatorial supra-Laplacian matrix of the multilayer network in detail, and we thereby show that the heterogeneity of interlayer edges and, especially, the fraction of missing edges crucially modify the spectral properties of the multilayer network. We illustrate our results with both synthetic network models and real data sets obtained from resting state magnetoencephalography. Our work demonstrates an important issue in the construction of frequency-based multilayer brain networks.Comment: 13 pages, 8 figure

Brain networks under attack : robustness properties and the impact of lesions

A growing number of studies approach the brain as a complex network, the so-called ‘connectome’. Adopting this framework, we examine what types or extent of damage the brain can withstand—referred to as network ‘robustness’—and conversely, which kind of distortions can be expected after brain lesions. To this end, we review computational lesion studies and empirical studies investigating network alterations in brain tumour, stroke and traumatic brain injury patients. Common to these three types of focal injury is that there is no unequivocal relationship between the anatomical lesion site and its topological characteristics within the brain network. Furthermore, large-scale network effects of these focal lesions are compared to those of a widely studied multifocal neurodegenerative disorder, Alzheimer’s disease, in which central parts of the connectome are preferentially affected. Results indicate that human brain networks are remarkably resilient to different types of lesions, compared to other types of complex networks such as random or scale-free networks. However, lesion effects have been found to depend critically on the topological position of the lesion. In particular, damage to network hub regions—and especially those connecting different subnetworks—was found to cause the largest disturbances in network organization. Regardless of lesion location, evidence from empirical and computational lesion studies shows that lesions cause significant alterations in global network topology. The direction of these changes though remains to be elucidated. Encouragingly, both empirical and modelling studies have indicated that after focal damage, the connectome carries the potential to recover at least to some extent, with normalization of graph metrics being related to improved behavioural and cognitive functioning. To conclude, we highlight possible clinical implications of these findings, point out several methodological limitations that pertain to the study of brain diseases adopting a network approach, and provide suggestions for future research

Controllability of structural brain networks.

Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function

Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material

The envirome and the connectome: exploring the structural noise in the human brain associated with socioeconomic deprivation

Complex cognitive functions are widely recognized to be the result of a number of brain regions working together as large-scale networks. Recently, complex network analysis has been used to characterize various structural properties of the large scale network organization of the brain. For example, the human brain has been found to have a modular architecture i.e. regions within the network form communities (modules) with more connections between regions within the community compared to regions outside it. The aim of this study was to examine the modular and overlapping modular architecture of the brain networks using complex network analysis. We also examined the association between neighborhood level deprivation and brain network structure – modularity and grey nodes. We compared network structure derived from anatomical MRI scans of 42 middle-aged neurologically healthy men from the least (LD) and the most deprived (MD) neighborhoods of Glasgow with their corresponding random networks. Cortical morphological covariance networks were constructed from the cortical thickness derived from the MRI scans of the brain. For a given modularity threshold, networks derived from the MD group showed similar number of modules compared to their corresponding random networks, while networks derived from the LD group had more modules compared to their corresponding random networks. The MD group also had fewer grey nodes – a measure of overlapping modular structure. These results suggest that apparent structural difference in brain networks may be driven by differences in cortical thicknesses between groups. This demonstrates a structural organization that is consistent with a system that is less robust and less efficient in information processing. These findings provide some evidence of the relationship between socioeconomic deprivation and brain network topology