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      Efficiency and Cost of Economical Brain Functional Networks

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      PLoS Computational Biology

      Public Library of Science

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          Abstract

          Brain anatomical networks are sparse, complex, and have economical small-world properties. We investigated the efficiency and cost of human brain functional networks measured using functional magnetic resonance imaging (fMRI) in a factorial design: two groups of healthy old ( N = 11; mean age = 66.5 years) and healthy young ( N = 15; mean age = 24.7 years) volunteers were each scanned twice in a no-task or “resting” state following placebo or a single dose of a dopamine receptor antagonist (sulpiride 400 mg). Functional connectivity between 90 cortical and subcortical regions was estimated by wavelet correlation analysis, in the frequency interval 0.06–0.11 Hz, and thresholded to construct undirected graphs. These brain functional networks were small-world and economical in the sense of providing high global and local efficiency of parallel information processing for low connection cost. Efficiency was reduced disproportionately to cost in older people, and the detrimental effects of age on efficiency were localised to frontal and temporal cortical and subcortical regions. Dopamine antagonism also impaired global and local efficiency of the network, but this effect was differentially localised and did not interact with the effect of age. Brain functional networks have economical small-world properties—supporting efficient parallel information transfer at relatively low cost—which are differently impaired by normal aging and pharmacological blockade of dopamine transmission.

          Author Summary

          It is increasingly evident that many complex networks, in diverse fields and over a wide range of spatial and time scales, may have topological properties in common. These unifying organizational principles have been described in terms of “small-world” parameters—meaning that many networks have both local clustering of connections and a short path length between any pair of nodes. Recent work has shown that we can also define small-world networks as having high global and local efficiency of parallel information transfer; and that many networks are economical in the sense of supporting high efficiency for low cost. Here we extend these ideas for the first time to an analysis of human brain functional networks derived from functional magnetic resonance imaging data. We show that human brain functional networks have economical small-world properties and that economical performance of these networks is detrimentally but differently affected by normal aging and by treatment with a dopamine receptor antagonist. The results illustrate concepts and techniques that could be important in further exploration of developmental, pathological, and pharmacological effects on human brain functional networks. They are also likely to be generalisable to applications in other fields of computational biology.

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          Most cited references 54

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          Collective dynamics of 'small-world' networks.

          Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
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            Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain.

            An anatomical parcellation of the spatially normalized single-subject high-resolution T1 volume provided by the Montreal Neurological Institute (MNI) (D. L. Collins et al., 1998, Trans. Med. Imag. 17, 463-468) was performed. The MNI single-subject main sulci were first delineated and further used as landmarks for the 3D definition of 45 anatomical volumes of interest (AVOI) in each hemisphere. This procedure was performed using a dedicated software which allowed a 3D following of the sulci course on the edited brain. Regions of interest were then drawn manually with the same software every 2 mm on the axial slices of the high-resolution MNI single subject. The 90 AVOI were reconstructed and assigned a label. Using this parcellation method, three procedures to perform the automated anatomical labeling of functional studies are proposed: (1) labeling of an extremum defined by a set of coordinates, (2) percentage of voxels belonging to each of the AVOI intersected by a sphere centered by a set of coordinates, and (3) percentage of voxels belonging to each of the AVOI intersected by an activated cluster. An interface with the Statistical Parametric Mapping package (SPM, J. Ashburner and K. J. Friston, 1999, Hum. Brain Mapp. 7, 254-266) is provided as a freeware to researchers of the neuroimaging community. We believe that this tool is an improvement for the macroscopical labeling of activated area compared to labeling assessed using the Talairach atlas brain in which deformations are well known. However, this tool does not alleviate the need for more sophisticated labeling strategies based on anatomical or cytoarchitectonic probabilistic maps.
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              Exploring complex networks.

               S Strogatz (2001)
              The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                pcbi
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                February 2007
                2 February 2007
                : 3
                : 2
                Affiliations
                Brain Mapping Unit, Department of Psychiatry, Addenbrooke's Hospital, University of Cambridge, Cambridge, United Kingdom
                University College London, United Kingdom
                Author notes
                * To whom correspondence should be addressed. E-mail: etb23@ 123456cam.ac.uk
                Article
                06-PLCB-RA-0424R2 plcb-03-02-01
                10.1371/journal.pcbi.0030017
                1794324
                17274684
                Copyright: © 2007 Achard and Bullmore. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                Counts
                Pages: 10
                Categories
                Research Article
                Biochemistry
                Computational Biology
                Neuroscience
                Homo (Human)
                Custom metadata
                Achard S, Bullmore E (2007) Efficiency and cost of economical brain functional networks. PLoS Comput Biol 3(2): e17. doi: 10.1371/journal.pcbi.0030017

                Quantitative & Systems biology

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