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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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Evolved brain networks located within the LAU1 efficiency-complexity morphospace. (a) Two-dimensional projections of the three-dimensional morphospace. The coordinates (Ediff, Erout, CN) = (1, 1, 1) are the coordinates corresponding to the LAU1 network, and therefore the initial population is located very close to those coordinates (cf. figure 3). All points indicate the regions of morphospace explored by eight independent runs of the optimization algorithm, all starting with the same initial population but driven by eight distinct objective functions (see §2e(ii)). The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front. (b) Three-dimensional efficiency-communication morphospace. Blue and red points show the average trajectory of a randomized and latticized brain network, respectively, which are not subjected to the selective pressures imposed when exploring the different fronts. The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front.
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RSTB20130530F4: Evolved brain networks located within the LAU1 efficiency-complexity morphospace. (a) Two-dimensional projections of the three-dimensional morphospace. The coordinates (Ediff, Erout, CN) = (1, 1, 1) are the coordinates corresponding to the LAU1 network, and therefore the initial population is located very close to those coordinates (cf. figure 3). All points indicate the regions of morphospace explored by eight independent runs of the optimization algorithm, all starting with the same initial population but driven by eight distinct objective functions (see §2e(ii)). The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front. (b) Three-dimensional efficiency-communication morphospace. Blue and red points show the average trajectory of a randomized and latticized brain network, respectively, which are not subjected to the selective pressures imposed when exploring the different fronts. The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front.

Mentions: Figure 4 shows the regions of the morphospace explored during the evolution of the eight fronts, starting with a population of networks derived from the LAU1 network (see the electronic supplementary material, figures S1 and S2, for LAU2 and UTR datasets, respectively). Although the shape and extent of the regions explored by each evolving front vary across datasets, we find three important aspects that are consistent, regardless of the dataset used to derive the initial population. First, the evolutionary algorithm is unable to find solutions within the region defined by {Ediff < 1}. Second, none of the fronts follows the trajectory of a randomization or latticization process. This demonstrates that the evolution of the network populations towards different regions of the morphospace is driven by distinct selection pressures, and not by the random nature of the rewiring algorithm. Third, the evolutionary process is able to generate brain-like networks within the region {Ediff > 1, Erout > 1, CN > 1}; that is, all three topological aspects of brain networks can simultaneously increase, while preserving wiring cost.Figure 4.


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)

Evolved brain networks located within the LAU1 efficiency-complexity morphospace. (a) Two-dimensional projections of the three-dimensional morphospace. The coordinates (Ediff, Erout, CN) = (1, 1, 1) are the coordinates corresponding to the LAU1 network, and therefore the initial population is located very close to those coordinates (cf. figure 3). All points indicate the regions of morphospace explored by eight independent runs of the optimization algorithm, all starting with the same initial population but driven by eight distinct objective functions (see §2e(ii)). The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front. (b) Three-dimensional efficiency-communication morphospace. Blue and red points show the average trajectory of a randomized and latticized brain network, respectively, which are not subjected to the selective pressures imposed when exploring the different fronts. The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4150305&req=5

RSTB20130530F4: Evolved brain networks located within the LAU1 efficiency-complexity morphospace. (a) Two-dimensional projections of the three-dimensional morphospace. The coordinates (Ediff, Erout, CN) = (1, 1, 1) are the coordinates corresponding to the LAU1 network, and therefore the initial population is located very close to those coordinates (cf. figure 3). All points indicate the regions of morphospace explored by eight independent runs of the optimization algorithm, all starting with the same initial population but driven by eight distinct objective functions (see §2e(ii)). The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front. (b) Three-dimensional efficiency-communication morphospace. Blue and red points show the average trajectory of a randomized and latticized brain network, respectively, which are not subjected to the selective pressures imposed when exploring the different fronts. The grey-scale assigned to each network indicates the epoch in which it was created, with light grey corresponding to early epochs and darker grey to later epochs. Orange points correspond to the Pareto-front networks of the last epoch of each front.
Mentions: Figure 4 shows the regions of the morphospace explored during the evolution of the eight fronts, starting with a population of networks derived from the LAU1 network (see the electronic supplementary material, figures S1 and S2, for LAU2 and UTR datasets, respectively). Although the shape and extent of the regions explored by each evolving front vary across datasets, we find three important aspects that are consistent, regardless of the dataset used to derive the initial population. First, the evolutionary algorithm is unable to find solutions within the region defined by {Ediff < 1}. Second, none of the fronts follows the trajectory of a randomization or latticization process. This demonstrates that the evolution of the network populations towards different regions of the morphospace is driven by distinct selection pressures, and not by the random nature of the rewiring algorithm. Third, the evolutionary process is able to generate brain-like networks within the region {Ediff > 1, Erout > 1, CN > 1}; that is, all three topological aspects of brain networks can simultaneously increase, while preserving wiring cost.Figure 4.

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