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Brain Networks: Characteristics, Connectivity, and Complexity, Papers of Art

This essay explores the unique characteristics of brain networks, focusing on their connectivity and complexity. It highlights the dense yet sparse nature of cortical networks, the specific patterns of neuronal connectivity, and the relationship between anatomical and functional connectivity. The text also discusses the plasticity of brain networks and the importance of considering both structural and functional aspects in neural analysis. Olaf sporns from indiana university is cited as a leading researcher in this field.

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Network Analysis, Complexity,
and Brain Function
Throughout the early history of neurology and neuroscience, most theoretical
accounts of brain function have emphasized either aspects of localization or
distributed properties [1]. Instead, modern views focus extensively on the struc-
ture and dynamics of large-scale neuronal networks, especially those of the cerebral
cortex and associated thalamocortical circuits whose activation underlies human
perception and cognition [2,3]. Both, localized and distributed aspects of brain
function naturally emerge from this network perspective. This essay highlights
several unique characteristics of brain networks and explores how a computational
analysis of these networks (see also [4]) may impact on our understanding of human
brain function.
With a few notable exceptions (such as diffusible messengers), all communication
between nerve cells is carried out along physical connections, often linking cells that
are separated by large distances. Signals within these connections consist of series of
action potentials (spikes) of unit magnitude and duration. The arrival of an action
potential at a synaptic junction triggers numerous biochemical and biophysical
processes, ultimately resulting in transmission of electrical signals to the postsyn-
aptic (receiving) cell, which may in turn generate an output spike transmitted along
the neuron’s axon. Neurons in the cerebral cortex maintain thousands of input and
output connections with other neurons, forming a dense network of connectivity
spanning the entire thalamocortical system. According to a detailed quantitative
study [5], the human cerebral cortex contains approximately 8.3 10
9
neurons and
6.7 10
13
connections. The length of all connections within a single human brain is
estimated between 100,000 and 10,000,000 km [5]. Despite this massive connectivity,
cortical networks are exceedingly sparse, with an overall connectivity factor (number
of connections present out of all possible) of around 10
6
. Brain networks are not
random, but form highly specific patterns. A predominant feature of brain networks
is that neurons tend to connect predominantly with other neurons in local groups.
Thus, local connectivity ratios can be significantly higher than those suggested by
random topology.
Networks in the brain can be analyzed at multiple levels of scale. Within small and
localized region of the brain, neurons form characteristic sets of connections, so-
called local circuits [6]. For example, neurons forming cortical columns show specific
patterns of connectivity between morphologically and pharmacologically distinct
classes of cells in different layers. At a higher level of scale, such columns commu-
nicate through “tangential” or “horizontal” connections, forming networks of col-
umns within single cortical areas. Connection patterns formed by these local, intra-
areal networks are thought to be responsible for the specific processing requirements
OLAF SPORNS
Olaf Sporns is at the Department of
Psychology and Programs in Cognitive
and Neural Science at Indiana
University, Bloomington. His main
research interest is theoretical and
computational modeling of the brain.
His past work has included the role of
neural synchrony in vision,
sensorimotor coordination,
neurorobotics, models of learning and
plasticity, and statistical measures of
complexity and network dynamics. His
homepage and publications are at
http://php.indiana.edu/~osporns.
E-mail: osporns@indiana.edu.
56 COMPLEXITY © 2003 Wiley Periodicals, Inc., Vol. 8, No. 1
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Network Analysis, Complexity,

and Brain Function

T

hroughout the early history of neurology and neuroscience, most theoretical accounts of brain function have emphasized either aspects of localization or distributed properties [1]. Instead, modern views focus extensively on the struc- ture and dynamics of large-scale neuronal networks, especially those of the cerebral cortex and associated thalamocortical circuits whose activation underlies human perception and cognition [2,3]. Both, localized and distributed aspects of brain function naturally emerge from this network perspective. This essay highlights several unique characteristics of brain networks and explores how a computational analysis of these networks (see also [4]) may impact on our understanding of human brain function. With a few notable exceptions (such as diffusible messengers), all communication between nerve cells is carried out along physical connections, often linking cells that are separated by large distances. Signals within these connections consist of series of action potentials (spikes) of unit magnitude and duration. The arrival of an action potential at a synaptic junction triggers numerous biochemical and biophysical processes, ultimately resulting in transmission of electrical signals to the postsyn- aptic (receiving) cell, which may in turn generate an output spike transmitted along the neuron’s axon. Neurons in the cerebral cortex maintain thousands of input and output connections with other neurons, forming a dense network of connectivity spanning the entire thalamocortical system. According to a detailed quantitative study [5], the human cerebral cortex contains approximately 8.3  109 neurons and 6.7  1013 connections. The length of all connections within a single human brain is estimated between 100,000 and 10,000,000 km [5]. Despite this massive connectivity, cortical networks are exceedingly sparse, with an overall connectivity factor (number of connections present out of all possible) of around 10^6. Brain networks are not random, but form highly specific patterns. A predominant feature of brain networks is that neurons tend to connect predominantly with other neurons in local groups. Thus, local connectivity ratios can be significantly higher than those suggested by random topology. Networks in the brain can be analyzed at multiple levels of scale. Within small and localized region of the brain, neurons form characteristic sets of connections, so- called local circuits [6]. For example, neurons forming cortical columns show specific patterns of connectivity between morphologically and pharmacologically distinct classes of cells in different layers. At a higher level of scale, such columns commu- nicate through “tangential” or “horizontal” connections, forming networks of col- umns within single cortical areas. Connection patterns formed by these local, intra- areal networks are thought to be responsible for the specific processing requirements

OLAF SPORNS

Olaf Sporns is at the Department of Psychology and Programs in Cognitive and Neural Science at Indiana University, Bloomington. His main research interest is theoretical and computational modeling of the brain. His past work has included the role of neural synchrony in vision, sensorimotor coordination, neurorobotics, models of learning and plasticity, and statistical measures of complexity and network dynamics. His homepage and publications are at http://php.indiana.edu/~osporns. E-mail: osporns@indiana.edu.

56 C O M P L E X I T Y © 2003 Wiley Periodicals, Inc., Vol. 8, No. 1

of each area (e.g., [7]). In visual cortex, for example, intra-areal connections within and across columns preferen- tially link neurons that share similar re- sponse properties. Considering the en- tire brain, the large-scale organization of the cortex is characterized by pat- terns of interconnections linking brain areas within and between specific sen- sory and motor systems (e.g., [8]). These connection pathways form networks that are species-characteristic, reflect- ing specific evolutionary adaptations. Neural connections are formed through developmental processes that at least in part are dependent upon neural activity [9]. Many brain networks remain plastic throughout the lifetime of the organism, exhibiting specific modifications of synaptic efficacy at multiple time scales as well as continu- ous morphological change. Thus, the detailed structural organization of brain networks will to some extent reflect the developmental and experiential history of the individual organism [10 – 12]. This point deserves special emphasis. Al- though it is possible (and perhaps de- sirable) to analyze brain networks as static entities, without reference to how they were generated, it is nonetheless essential to realize that their fine struc- ture and morphology is the result of continuous interaction between neural substrate, ongoing neuronal activity and embodied action of an individual organism within an environment.

ANATOMICAL AND FUNCTIONAL

CONNECTIVITY

Because of the close relationship be- tween neural connectivity and neural activity throughout the brain, it is im- portant to consider structural connec- tion patterns within the context of the specific patterns of dynamic (“func- tional”) interactions they support. The closeness and intricacy of this relation- ship is perhaps unique among natural and artificial networks. Thus, our first distinction is that between anatomical (structural) and functional connectivity.

Anatomical connectivity simply re- fers to the set of physical or structural connections linking neuronal units at a given time. In any structural analysis of neural connection patterns, a choice has to be made on the level of the spa- tial scale at which the analysis is to be performed. Analyses carried out at the local circuit level would most likely focus on the pattern of synaptic con- nections between individual neurons. Analyses of intra-areal patterns of con- nections would involve “connection bundles” or “synaptic patches” linking local neuronal populations (neuronal groups or columns). Analyses of large- scale connection patterns would focus on connection pathways linking segre- gated areas of the brain. Such pathways would comprise many thousands or millions of individual fibers. Functional connectivity refers to the pattern of temporal correlations (or, more generally, deviations from statis- tical independence) that exists between distinct neuronal units [13,14]. Such temporal correlations are often the re- sult of neuronal interactions along ana- tomical or structural connections; in some cases observed correlations may be due to common input from an exter- nal neuronal or stimulus source. Devi- ations from statistical independence between neuronal elements are com- monly captured in a covariance matrix (or a correlation matrix), which, under certain statistical assumptions, may be viewed as a representation of the sys- tem’s functional connectivity. Although temporal correlations are perhaps most often used to represent statistical pat- terns in neuronal networks, other mea- sures such as spectral coherence or consistency in relative phase relation- ships [15] may also serve as indicators of functional connectivity. The relationship between structural and functional dimensions of brain connectivity is mutual and reciprocal. It is easy to see that structural connectiv- ity is a major constraint on the kinds of patterns of functional connectivity that

can be generated. In the other direction, functional interactions can contribute to the shaping of the underlying ana- tomical substrate. This is accomplished either directly through activity (covari- ance)-dependent synaptic modifica- tion, or, over longer time scales, through effects of functional connectiv- ity on an organism’s perceptual, cogni- tive or behavioral capabilities, which in turn affect adaptation and survival. The reciprocity between anatomical and functional networks deserves emphasis as it captures some of the unique as- pects of brain networks.

SEGREGATION AND INTEGRATION IN

THE BRAIN

The networks of the cerebral cortex ex- hibit two main principles of structural and functional organization, segrega- tion and integration [16 – 18]. Anatomi- cal and functional segregation refers to the existence of specialized neurons and brain areas, often organized into distinct neuronal populations (groups or columns) or cortical areas. These specialized and segregated sets of neu- rons selectively respond to specific in- put features (such as orientation, spatial frequency, or wavelength), or conjunc- tions of features (such as faces). They reside in cortical areas that process sep- arate feature dimensions (such as color and motion) or sensory modalities. However, segregated and specialized neuronal units do not operate in isola- tion. There is abundant evidence that coherent perceptual and cognitive states require the coordinated activa- tion, that is, the functional integration, of very large numbers of neurons within the distributed system of the cerebral cortex [19,20]. Electrophysiological studies have shown that perceptual or cognitive states are associated with spe- cific and highly dynamic (short-lasting) patterns of temporal correlations (func- tional connectivity) between different regions of the thalamocortical system [21]. Human neuroimaging experi- ments have revealed that virtually all perceptual or cognitive tasks, for exam-

© 2003 Wiley Periodicals, Inc. C O M P L E X I T Y 57

used as cost functions in simulations de- signed to optimize network architectures. Networks optimized for high complexity show structural motifs that are very sim- ilar to those observed in real cortical con- nection matrices [4,30], in particular a tendency to form clusters, short charac- teristic path lengths, and short wiring lengths. Other measures produce net- works with strikingly different structural characteristics. These results open up an interesting new perspective on the role of complexity in evolution. Although it is unrealistic to assume that complexity could be directly used as a cost function during natural selection, it is possible that an increased ability of neuronal networks to combine functional segregation (generation of spe- cialized neural circuits maximizing infor- mation transfer) together with their func- tional integration (generation of temporal correlations across feature domains and modalities) was favored. Thus, the con- comitant increase in complexity could have driven morphological change in a direction that is consistent with the pat- terns of cortical connectivity we actually observe.

FROM NETWORKS TO COGNITION

The structure of brain networks is a re- sult of the combined forces of natural

selection and neural activity during evolution and development. From a computational and information theo- retical perspective, two of the major problems brains have to solve are the extraction of information (statistical regularities) from inputs and the gener- ation of coherent states that allow coor- dinated perception and action in real time. Solutions to these problems are

reflected in the dual organizational principles of functional segregation and functional integration found throughout the cerebral cortex. The requirement to achieve segregation and integration simultaneously im- poses severe constraints on the set of possible cortical connection patterns. Much more empirical and computa- tional work is needed to elucidate the

functional principles shaping struc- tural connection patterns in the cor- tex. Our own computer simulations (reviewed in more detail in [4,30]) sug- gest that networks that optimally combine segregation and integration have structural motifs that are very similar to the ones present in large- scale cortical systems. Very likely there are many more ways in which structural properties of brain networks impact upon the dy- namical and informational patterns neurons can generate and maintain. There is mounting evidence that dy- namical patterns generated by brain networks underlie all of cognition and perception (see e.g. [2,15,21,22]. At least some aspects of vision seem to be em- bedded in the structural connectivity of parts of the thalamocortical system [33,34], and disruptions of the wiring of these networks result in severe and spe- cific alterations of mental and percep- tual function. The nature of awareness and consciousness itself may be rooted in the rapid integration of information [35,36], requiring a structural network capable of sustaining this process. Net- work analysis may be the key to under- standing and harnessing the remark- able computational and informational power of the brain.

REFERENCES

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From a computational and

information theoretical

perspective, two of the major

problems brains have to solve

are the extraction of information

(statistical regularities) from

inputs and the generation of

coherent states that allow

coordinated perception and action

in real time.

© 2003 Wiley Periodicals, Inc. C O M P L E X I T Y 59

  1. Varela, F.; Lachaux, J.-P.; Rodriguez, E.; Martinerie, J. The brainweb: Phase synchronization and large-scale integration. Nat Rev Neurosci 2001, 2, 229 – 239.
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60 C O M P L E X I T Y © 2003 Wiley Periodicals, Inc.