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Using Pareto optimality to explore the topology and dynamics of the human connectome.

Avena-Koenigsberger A, Goñi J, Betzel RF, van den Heuvel MP, Griffa A, Hagmann P, Thiran JP, Sporns O - Philos. Trans. R. Soc. Lond., B, Biol. Sci. (2014)

Bottom Line: This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance.Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost.This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA.

ABSTRACT
Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

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Consistent changes in connection patterns observed in fronts 1 through 4 across all three datasets. (a) Density of empirical and evolved networks. (b) New connections (red points) in evolved networks tend to extend over long spatial distances; fibre densities that are weakened during evolution (blue points) tend to involve pairs of nodes that are spatially close or belong to the same anatomical region. (c) High-cost connections are principal targets for rewiring during the evolutionary process.
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RSTB20130530F6: Consistent changes in connection patterns observed in fronts 1 through 4 across all three datasets. (a) Density of empirical and evolved networks. (b) New connections (red points) in evolved networks tend to extend over long spatial distances; fibre densities that are weakened during evolution (blue points) tend to involve pairs of nodes that are spatially close or belong to the same anatomical region. (c) High-cost connections are principal targets for rewiring during the evolutionary process.

Mentions: Other aspects of changes in connection patterns were consistently observed across all three datasets. First, the density of evolved networks in all four fronts increases significantly (figure 6a), indicating that areas originally unconnected have a strong tendency to become weakly connected. These new projections appear as a result of rewiring of edges away from denser pathways, thus sculpting their overall pattern into a new topology and steering the population towards one of the four Pareto fronts. Second, most of these newly formed projections extend over long spatial distances, while most of the projections that become weakened involve nodes that are spatially close, including node pairs that belong to the same anatomical region (figure 6b). Finally, a cost analysis suggests that high-cost connections, i.e. connections that contribute strongly to the overall cost of the network (which is conserved in our simulations) are principal targets for rewiring (figure 6c). Their rewiring results in a dispersal of their contribution to network cost to a larger set of connections spanning a greater number of anatomical regions.Figure 6.


Using Pareto optimality to explore the topology and dynamics of the human connectome.

Avena-Koenigsberger A, Goñi J, Betzel RF, van den Heuvel MP, Griffa A, Hagmann P, Thiran JP, Sporns O - Philos. Trans. R. Soc. Lond., B, Biol. Sci. (2014)

Consistent changes in connection patterns observed in fronts 1 through 4 across all three datasets. (a) Density of empirical and evolved networks. (b) New connections (red points) in evolved networks tend to extend over long spatial distances; fibre densities that are weakened during evolution (blue points) tend to involve pairs of nodes that are spatially close or belong to the same anatomical region. (c) High-cost connections are principal targets for rewiring during the evolutionary process.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4150305&req=5

RSTB20130530F6: Consistent changes in connection patterns observed in fronts 1 through 4 across all three datasets. (a) Density of empirical and evolved networks. (b) New connections (red points) in evolved networks tend to extend over long spatial distances; fibre densities that are weakened during evolution (blue points) tend to involve pairs of nodes that are spatially close or belong to the same anatomical region. (c) High-cost connections are principal targets for rewiring during the evolutionary process.
Mentions: Other aspects of changes in connection patterns were consistently observed across all three datasets. First, the density of evolved networks in all four fronts increases significantly (figure 6a), indicating that areas originally unconnected have a strong tendency to become weakly connected. These new projections appear as a result of rewiring of edges away from denser pathways, thus sculpting their overall pattern into a new topology and steering the population towards one of the four Pareto fronts. Second, most of these newly formed projections extend over long spatial distances, while most of the projections that become weakened involve nodes that are spatially close, including node pairs that belong to the same anatomical region (figure 6b). Finally, a cost analysis suggests that high-cost connections, i.e. connections that contribute strongly to the overall cost of the network (which is conserved in our simulations) are principal targets for rewiring (figure 6c). Their rewiring results in a dispersal of their contribution to network cost to a larger set of connections spanning a greater number of anatomical regions.Figure 6.

Bottom Line: This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance.Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost.This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

View Article: PubMed Central - PubMed

Affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA.

ABSTRACT
Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

Show MeSH