9,273 research outputs found
Hierarchical modularity in human brain functional networks
The idea that complex systems have a hierarchical modular organization
originates in the early 1960s and has recently attracted fresh support from
quantitative studies of large scale, real-life networks. Here we investigate
the hierarchical modular (or "modules-within-modules") decomposition of human
brain functional networks, measured using functional magnetic resonance imaging
(fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a
customized template to extract networks with more than 1800 regional nodes, and
we applied a fast algorithm to identify nested modular structure at several
hierarchical levels. We used mutual information, 0 < I < 1, to estimate the
similarity of community structure of networks in different subjects, and to
identify the individual network that is most representative of the group.
Results show that human brain functional networks have a hierarchical modular
organization with a fair degree of similarity between subjects, I=0.63. The
largest 5 modules at the highest level of the hierarchy were medial occipital,
lateral occipital, central, parieto-frontal and fronto-temporal systems;
occipital modules demonstrated less sub-modular organization than modules
comprising regions of multimodal association cortex. Connector nodes and hubs,
with a key role in inter-modular connectivity, were also concentrated in
association cortical areas. We conclude that methods are available for
hierarchical modular decomposition of large numbers of high resolution brain
functional networks using computationally expedient algorithms. This could
enable future investigations of Simon's original hypothesis that hierarchy or
near-decomposability of physical symbol systems is a critical design feature
for their fast adaptivity to changing environmental conditions
Modular and Hierarchically Modular Organization of Brain Networks
Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data
Resolving Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations
Human brain anatomy and function display a combination of modular and
hierarchical organization, suggesting the importance of both cohesive
structures and variable resolutions in the facilitation of healthy cognitive
processes. However, tools to simultaneously probe these features of brain
architecture require further development. We propose and apply a set of methods
to extract cohesive structures in network representations of brain connectivity
using multi-resolution techniques. We employ a combination of soft
thresholding, windowed thresholding, and resolution in community detection,
that enable us to identify and isolate structures associated with different
weights. One such mesoscale structure is bipartivity, which quantifies the
extent to which the brain is divided into two partitions with high connectivity
between partitions and low connectivity within partitions. A second,
complementary mesoscale structure is modularity, which quantifies the extent to
which the brain is divided into multiple communities with strong connectivity
within each community and weak connectivity between communities. Our methods
lead to multi-resolution curves of these network diagnostics over a range of
spatial, geometric, and structural scales. For statistical comparison, we
contrast our results with those obtained for several benchmark null models. Our
work demonstrates that multi-resolution diagnostic curves capture complex
organizational profiles in weighted graphs. We apply these methods to the
identification of resolution-specific characteristics of healthy weighted graph
architecture and altered connectivity profiles in psychiatric disease.Comment: Comments welcom
Development of modularity in the neural activity of children's brains
We study how modularity of the human brain changes as children develop into
adults. Theory suggests that modularity can enhance the response function of a
networked system subject to changing external stimuli. Thus, greater cognitive
performance might be achieved for more modular neural activity, and modularity
might likely increase as children develop. The value of modularity calculated
from fMRI data is observed to increase during childhood development and peak in
young adulthood. Head motion is deconvolved from the fMRI data, and it is shown
that the dependence of modularity on age is independent of the magnitude of
head motion. A model is presented to illustrate how modularity can provide
greater cognitive performance at short times, i.e.\ task switching. A fitness
function is extracted from the model. Quasispecies theory is used to predict
how the average modularity evolves with age, illustrating the increase of
modularity during development from children to adults that arises from
selection for rapid cognitive function in young adults. Experiments exploring
the effect of modularity on cognitive performance are suggested. Modularity may
be a potential biomarker for injury, rehabilitation, or disease.Comment: 29 pages, 11 figure
From Caenorhabditis elegans to the Human Connectome: A Specific Modular Organisation Increases Metabolic, Functional, and Developmental Efficiency
The connectome, or the entire connectivity of a neural system represented by
network, ranges various scales from synaptic connections between individual
neurons to fibre tract connections between brain regions. Although the
modularity they commonly show has been extensively studied, it is unclear
whether connection specificity of such networks can already be fully explained
by the modularity alone. To answer this question, we study two networks, the
neuronal network of C. elegans and the fibre tract network of human brains
yielded through diffusion spectrum imaging (DSI). We compare them to their
respective benchmark networks with varying modularities, which are generated by
link swapping to have desired modularity values but otherwise maximally random.
We find several network properties that are specific to the neural networks and
cannot be fully explained by the modularity alone. First, the clustering
coefficient and the characteristic path length of C. elegans and human
connectomes are both higher than those of the benchmark networks with similar
modularity. High clustering coefficient indicates efficient local information
distribution and high characteristic path length suggests reduced global
integration. Second, the total wiring length is smaller than for the
alternative configurations with similar modularity. This is due to lower
dispersion of connections, which means each neuron in C. elegans connectome or
each region of interest (ROI) in human connectome reaches fewer ganglia or
cortical areas, respectively. Third, both neural networks show lower
algorithmic entropy compared to the alternative arrangements. This implies that
fewer rules are needed to encode for the organisation of neural systems
Influence of wiring cost on the large-scale architecture of human cortical connectivity
In the past two decades some fundamental properties of cortical connectivity have been discovered: small-world structure, pronounced hierarchical and modular organisation, and strong core and rich-club structures. A common assumption when interpreting results of this kind is that the observed structural properties are present to enable the brain's function. However, the brain is also embedded into the limited space of the skull and its wiring has associated developmental and metabolic costs. These basic physical and economic aspects place separate, often conflicting, constraints on the brain's connectivity, which must be characterized in order to understand the true relationship between brain structure and function. To address this challenge, here we ask which, and to what extent, aspects of the structural organisation of the brain are conserved if we preserve specific spatial and topological properties of the brain but otherwise randomise its connectivity. We perform a comparative analysis of a connectivity map of the cortical connectome both on high- and low-resolutions utilising three different types of surrogate networks: spatially unconstrained (‘random’), connection length preserving (‘spatial’), and connection length optimised (‘reduced’) surrogates. We find that unconstrained randomisation markedly diminishes all investigated architectural properties of cortical connectivity. By contrast, spatial and reduced surrogates largely preserve most properties and, interestingly, often more so in the reduced surrogates. Specifically, our results suggest that the cortical network is less tightly integrated than its spatial constraints would allow, but more strongly segregated than its spatial constraints would necessitate. We additionally find that hierarchical organisation and rich-club structure of the cortical connectivity are largely preserved in spatial and reduced surrogates and hence may be partially attributable to cortical wiring constraints. In contrast, the high modularity and strong s-core of the high-resolution cortical network are significantly stronger than in the surrogates, underlining their potential functional relevance in the brain
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