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The economy of brain network organization

Key Points

  • Cost control and complex topology are important aspects of the organization of human and other nervous systems.

  • Efficient transfer of information between modules of brain networks confers functional advantages in terms of adaptive behaviour, but it imposes a premium in terms of wiring cost.

  • Brain networks negotiate an economical trade-off between minimizing wiring cost and maximizing expensive but advantageous topological properties such as efficiency.

  • Brain networks can renegotiate trade-offs between cost and efficiency dynamically over short and long timescales.

  • High-cost components of human brain networks may be particularly vulnerable to abnormal development or pathological attack, leading to disorders of cognition or behaviour.

Abstract

The brain is expensive, incurring high material and metabolic costs for its size — relative to the size of the body — and many aspects of brain network organization can be mostly explained by a parsimonious drive to minimize these costs. However, brain networks or connectomes also have high topological efficiency, robustness, modularity and a 'rich club' of connector hubs. Many of these and other advantageous topological properties will probably entail a wiring-cost premium. We propose that brain organization is shaped by an economic trade-off between minimizing costs and allowing the emergence of adaptively valuable topological patterns of anatomical or functional connectivity between multiple neuronal populations. This process of negotiating, and re-negotiating, trade-offs between wiring cost and topological value continues over long (decades) and short (millisecond) timescales as brain networks evolve, grow and adapt to changing cognitive demands. An economical analysis of neuropsychiatric disorders highlights the vulnerability of the more costly elements of brain networks to pathological attack or abnormal development.

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Figure 1: Allometric and fractal scaling of brains and human brain networks.
Figure 2: Hubs and modules in the brain.
Figure 3: Economical trade-offs between wiring cost and topological efficiency of brain networks.
Figure 4: Brain disorders affect high-cost components of networks.

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Acknowledgements

The Behavioural and Clinical Neuroscience Institute, University of Cambridge, is supported by the Medical Research Council (UK) and the Wellcome Trust.

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Correspondence to Ed Bullmore or Olaf Sporns.

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Ed Bullmore is a part-time employee and stockholder of GlaxoSmithKline. Olaf Sporns declares no competing financial interests.

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Glossary

Graphs

Simple models of a system that are based on a set of nodes and the edges between them. The nodes represent agents or elements, and the edges represent interactions or connections between nodes.

Topology

Applied to a network, the layout pattern of interconnections, defined in terms of the relations of nodes and edges.

Robustness

The degree to which the topological properties of a network are resilient to 'lesions' such as the removal of nodes or edges.

Hub

A topologically important or central node, as defined by one of several possible measures of centrality, including degree centrality (number of edges) or betweenness centrality.

Wiring cost

The fixed cost of making anatomical connections between neurons, often approximated by the wiring volume of anatomical connections.

Efficiency

A topological measure of the reciprocal or inverse of the path length between nodes. In brain networks, global efficiency is often used as a measure of the overall capacity for parallel information transfer and integrated processing.

Economy

Applied to brain network organization, economy refers to the careful management of resources in the service of delivering robust and efficient performance.

Allometric scaling

Allometric scaling concerns the relationships between body size (scale) and other anatomical, functional or metabolic properties of organisms. These scaling relationships are often described by power laws.

Connection distances

Spatial measures that describe the physical distance between nodes that are connected by an edge in the network; often approximated as the Euclidean distance between nodes.

Functional connectivity

Statistical association — for example, significant correlations — between neurophysiological measurements recorded from anatomically distinct neurons or regions at several time points.

Edges

In a brain graph, an edge between nodes (regions or neurons) indicates that the nodes are anatomically or functionally connected.

Path length

A measure of network topology. In a binary graph, the path length between two nodes is the minimum number of edges that must be traversed to get from one node to another.

Sparse coding

A type of neural coding that represents information by the activation of a small subset of the available neurons and/or by activation of neurons over a brief instant of time.

Connection density

A topological measure that describes the number of edges in a network as a proportion of the maximum possible number of edges, namely (N2N)/2 for an undirected network of N nodes.

Small world

A term used to describe complex networks that have a combination of both random and regular topological properties; that is, high efficiency (short path-length) and high clustering, respectively.

Clustering

A measure of that captures the 'cliquishness' of a local neighbourhood, based on the number of triangular connections between groups of three nodes.

Community structure

The sub-global organization of a complex network. Modularity is an example of community structure, but not all network communities are simply modular.

Heavy-tailed degree distributions

A term that is generally used to mean that the proportion of high-degree nodes (nodes with a large number of edges connecting them to other nodes (hubs)) is greater than that in random graphs.

Centrality

A topological measure of the importance or influence of a node or edge for network organization.

Critical dynamics

If a system is dynamically on the cusp of a phase transition between random and regular dynamics, it is said to be in a critical state or demonstrating critical dynamics.

Simulated annealing

A computer algorithm used to find a good approximation to the global optimum of a function over a large search space.

Connector hubs

Hubs that mediate a high proportion of inter-modular (often long-distance) connections.

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Bullmore, E., Sporns, O. The economy of brain network organization. Nat Rev Neurosci 13, 336–349 (2012). https://doi.org/10.1038/nrn3214

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