Sporns;
Networks of the Brain |
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When a person is cognitively at rest, quietly awake and alert, the brain engages in a characteristic pattern of dynamic neural activity. The spatiotemporal profile of this
pattern is molded by an intricate structural
network of nerve
fibers and pathways. |
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Changes in sensory input or cognitive task result in highly
specific patterns of brain
activation.
These patterns are the effects of dynamic
perturbations of a complex and continually active network. |
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Behavior and cognition change over development and the entire lifespan. The growth
and maturation of anatomical
connections in the brain modify the range of your
responses and cognitive
capacities. |
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Brain and body are dynamically
coupled
through continual cycles of action and perception. By causing bodily movement, brain
networks can structure
their own inputs and modulate their internal dynamics. |
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Network Measures and
Architectures |
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Graphs and Networks --
Definitions |
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A graph is a mathematical representation of a real world network or, more generally, of some system composed of interconnected
elements. |
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A simple graph comprises a set of nodes and a set of edges. |
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Edges can
be undirected or directed. |
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One of the most elementary representations of a graph is the adjacency matrix, also called a connection matrix. |
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Nodes can
be linked directly by a single edges or indirectly by sequences of intermediate nodes and edges. |
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Ordered sequences of unique edges and intermediate nodes are call paths. |
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Sequences of nonunique edges or
call walks. |
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Paths can connect a node to itself, in which case the path is called a cycle. |
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Local Segregation -- Clustering and Modularity |
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A large number of processing
characteristics and functional contributions of a node are determined by its
interactions within a local neighborhood. |
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The neighborhood is defined in terms of topological
distance and does not necessarily imply close physical proximity. |
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Several measures of local connectivity evaluate extent
to which the network is organized into the densely coupled
neighborhoods,
also known as clusters, communities, or modules. |
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Densely interconnected
neighborhoods form a cluster around the node, while sparsely interconnected
neighbors do not. |
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The average of the clustering
coefficients for each individual node is the clustering coefficient of the
graph. |
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Clustering, motifs, and modularity capture aspects of
the local connectivity structure of a graph. |
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Clustering
is significant in a neurobiological context
because neuronal units or brain regions that form a densely connected
cluster or module communicate a lot of shared information and are therefore likely to constitute a
functionally coherent
brain system. |
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Clustering
and modularity
highlight a particular aspect of the functional
organization of the brain, its tendency to
form segregated subsystems with specialized functional
properties. |
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Measures of the capacity of the network to engage in global interactions that transcend modules and enable network-wide
integration are based
on paths and distances between nodes. |
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One of the most commonly used measures of integration in brain networks is the characteristic path length, usually computed as the global
average of the graph's
distance matrix. |
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Hub nodes
are densely connected to the rest of the network, facilitate global integrative processes, or play a critical compensatory role when the network
is damaged. |
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In networks that are composed of
local communities or modules, within-module and between-modules connectivity can provide information about the specific contributions of individual nodes. |
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Several measures
of centrality are
based on the notion of shortest paths. |
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A node is central if it has great control over the flow of information within the network. |
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Power-law
degree distributions are shared across many networks and
indicate a "scale-free"
organization. |
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The term "scale-free" refers to the fact that a power-law distribution has no characteristic scale -- zooming in on any segment of the distribution does not
change its shape. |
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Brain Networks -- Structure and
Dynamics |
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Nervous systems are organized on multiple scales, from synaptic
connections between single
cells,
to the organization of cell populations within individual
anatomical regions, and finally to large-scale
architecture brain regions and their interconnecting pathways. |
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The multiscale aspect of the
nervous system is an essential feature of its organization and network
architecture. |
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Brain connectivity at the large-scale (among regions and systems) describes neural processes that are the outcome of dynamic coordination among smaller elements. |
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Structural
connectivity refers to a set of physical or structural (anatomical) connections linking neural
elements. |
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Functional
connectivity captures
patterns of deviations
from statistical independence between distributed and often spatially remote neuronal units. |
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Effective connectivity describes a network of causal effects between neural elements, which can be
inferred through time series analysis, statistical modeling, or experimental perturbations. |
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The close
relationship between structure and function in the brain can create some ambiguity as to whether a neural parameter is best
classified as structural or functional. |
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Neural communication is significantly affected by axonal conduction delays. |
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One of the most fundamental problems of graph analysis in the brain is the definition of nodes and edges. |
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Techniques
that resolve single
neurons
currently permit the observation of only a small number of cells embedded within a vast and mostly unobserved network. |
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All noninvasive techniques, while covering a large part of the brain, record signals that originate from neuronal populations. |
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All studies of structural and functional
brain networks require a parcellation of the recorded brain volume into distinct regions and connections. |
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Node definition generally involves an
anatomical parcellation into coherent
regions on
the basis of histological or imaging data. |
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Defining nodes as individual voxels in fMRI data or electrodes or sensors in electrophysiological or MEG experiments. |
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Edge
definition
involves the estimation of pairwise
associations between nodes. |
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The use of perturbations offers one approach for discerning
causal patterns. |
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The extraordinary
variety and complexity of neural network activity patterns requires computational
modeling of empirical
data to achieve an understanding of the system
that is both explanatory and predictive. |
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No experimental manipulation is devised without
recourse to some sort of model or representation of the essential
components and interactions and their expected behavior. |
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Dynamic connectivity-based
models are
indispensable for understanding how the local activity of neural units is coordinated
and integrated to achieve global
patterns. |
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The basis of all computational models is a set of state equations that govern the temporal
evolution of the dynamic variables. |
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Given a set of initial conditions, the trajectory of the system will flow toward a bounded set of points that constitute an attractor. |
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An attractor may be as simple as a single fixed point or have a more elaborate
geometric shape
such as limit cycles (in the case at periodic dynamics) or strange attractors (in the case
that chaotic dynamics). |
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The set of
points from which the system
slows to a given attractor is its basin of attraction. |
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In the history of neuroscience the concept of functional localization pitches
those who view brain function as resulting from action of specialized centers against those who conceptualize brain function as fundamentally nonlocal and distributed. |
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The functional
specialization of each
local element is determined in part by the intrinsic properties of the
element and in part by its extrinsic network interactions. |
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Mapping the anatomy of the brain networks offers important clues as to the functional
specialization of each of the network elements. |
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Connectivity
carries information about the functionality of elements in different kinds of biological networks. |
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Phrenology, the identification of psychological and personality traits on the basis of
protrusions or bumps on a person's skull, has been thoroughly debunked as a pseudoscience. |
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Brodmann's cortical maps and his regional classification remains an important reference
system for cortical
localization. |
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Karl Lashley's studies of the behavioral effects of ablations and white matter cuts in rat brain led him to reject localization of function and to emphasize the distributed nature of brain function. |
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Connectivity profiles and the resulting cross
correlation matrix identified clusters
of voxels with shared
connectivity patterns. |
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Parcellation
of Broca's area in
the left inferior frontal cortex. Broca's area appears segregated
into three distinct subregions, derived on the
basis of the similarities and dissimilarities of their long-range structural connections estimated from diffusion
imaging followed by computational
tractography. (diagram) |
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Connectivity-based parcellation, in conjunction with probabilistic maps of cellular microanatomy, has great promise for relating brain structure to function. |
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Variability in Brain
Connectivity |
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Variability
is an essential feature of many biological
systems,
and is one of the major driving forces of evolution. |
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A significant proportion of variable neuronal morphology and network structure is likely the result of experience- and activity-dependent processes. |
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Brain networks combine a strong tendency toward functional
homeostasis with the capacity to express variations in behavior. |
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Structurally variable but functionally equivalent networks, are an example of degeneracy, defined as the capacity
of systems to perform
similar functions despite differences in the way they are configured and connected. |
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Degeneracy
is widespread among biological
systems and can be found in molecular,
cellular, and large-scale networks. |
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Human brain networks display degeneracy, since different sets of brain regions can support
a given cognitive function. |
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Different individuals utilize different (degenerate) networks. |
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Individual brain regions may not be necessary or, alternatively, the recovery
processes following brain injury can configure structurally different but functionally
equivalent networks. |
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Degeneracy
in cognitive networks is suggestive of the idea that mechanisms promoting functional
homeostasis
may operate at the scale of the whole brain to ensure that structural variations or disturbances do not lead to uncontrolled divergence of functional outcomes. |
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Nervous systems exhibit striking diversity of neuronal cell types, distinguished by their characteristic cellular morphology. |
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Diversity
and variability in cortical interneurons has been
shown to affect network dynamics, with greater variability leading to less pronounced
network synchrony. |
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Diverse and
variable cell morphology may help to regulate
the excitability of nervous tissue, a potentially
important factor in preventing pathological
states such as epilepsy. |
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Heterogeneity
of interneurons has
been invoked as a source of greater "computational
power" for cortical
networks. |
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Anatomical tracing and staining techniques that
allow the visualization
of the fine structure of morphologically and physiologically identified neurons and local circuits has provided
abundant evidence that cells of different types form and maintain specific connection patterns. |
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Computational studies suggest that specific neuronal
morphologies --
e.g. dendritic branching patterns and synaptic
distributions -- support specific elementary computations. |
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As the cellular
architecture of the brain is probed with ever more refined
methods, the structure
of every neuron will reveal unique patterns of neuronal processes and intracellular junctions. |
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Homeostatic
and coordinative processes within the nervous system ensure that variability at molecular or cellular scales generally does not perturb processes unfolding on larger scales. |
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The modularity of brain's architecture effectively insulates functionally bound subsystems from spreading perturbations due to small fluctuations in structure or dynamics. |
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Individual neurons, even those belonging to the same class, must remain different from one another to
continually create dynamic variability as a substrate for adaptive
change. |
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