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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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Examples of low-resolution brain networks. (a) Low-resolution partition of the right hemisphere of the human cortex, composed of 33 anatomical areas. (b) Down-sampled connection weights (fibre densities) of LAU1 network. (c) Difference between the average networks of fronts 1 through 4, and the LAU1 network. Blue elements indicate negative sign; red elements indicate positive sign. (d) Consistent changes of connection strengths in evolved network populations: colours indicate whether fibre densities increased (red), decreased (blue) or changed in an unspecific direction (green) across 90% or more of the evolved networks belonging to one front.
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RSTB20130530F5: Examples of low-resolution brain networks. (a) Low-resolution partition of the right hemisphere of the human cortex, composed of 33 anatomical areas. (b) Down-sampled connection weights (fibre densities) of LAU1 network. (c) Difference between the average networks of fronts 1 through 4, and the LAU1 network. Blue elements indicate negative sign; red elements indicate positive sign. (d) Consistent changes of connection strengths in evolved network populations: colours indicate whether fibre densities increased (red), decreased (blue) or changed in an unspecific direction (green) across 90% or more of the evolved networks belonging to one front.

Mentions: To allow comparisons across datasets, brain networks were down-sampled into a commonly used low-resolution partition of the human cortex, composed of 66 anatomical areas [50], with 33 areas representing the right cortical hemisphere of the brain (see figure 5a). For each dataset, networks evolved towards eight fronts (10 repetitions per front) and the final populations of 500 evolved networks were down-sampled to the low-resolution partition and then aggregated according to front membership. Thus, we obtained eight populations (one for each front) of low-resolution brain networks, each population containing 5000 evolved brain networks. As the four fronts driving networks towards {Ediff < 1} failed to advance, their evolved networks were not investigated further. For the remaining four fronts, we identified anatomical pathways whose fibre density and/or cost has significantly changed during the evolutionary process to favour particular topological traits. For each front, all final populations of evolved networks were aggregated into a single average network, representative of the corresponding front. The differences between the average networks of each front and the corresponding empirical network are shown in figure 5c, together with the corresponding plots recording the consistency with which connections increased or decreased in strength (figure 5d). Each of the fronts is associated with a characteristic pattern of changes in connection weights, and visual inspection suggests greater similarity in the patterns for fronts 1 and 3, and for patterns for fronts 2 and 4, respectively. Analysis of the pairwise cosine angles between average networks of each front confirms this observation, with fronts 1 and 3 (both maximizing CN) and fronts 2 and 4 (both minimizing CN) exhibiting the greatest similarity across all three datasets.Figure 5.


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)

Examples of low-resolution brain networks. (a) Low-resolution partition of the right hemisphere of the human cortex, composed of 33 anatomical areas. (b) Down-sampled connection weights (fibre densities) of LAU1 network. (c) Difference between the average networks of fronts 1 through 4, and the LAU1 network. Blue elements indicate negative sign; red elements indicate positive sign. (d) Consistent changes of connection strengths in evolved network populations: colours indicate whether fibre densities increased (red), decreased (blue) or changed in an unspecific direction (green) across 90% or more of the evolved networks belonging to one front.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4150305&req=5

RSTB20130530F5: Examples of low-resolution brain networks. (a) Low-resolution partition of the right hemisphere of the human cortex, composed of 33 anatomical areas. (b) Down-sampled connection weights (fibre densities) of LAU1 network. (c) Difference between the average networks of fronts 1 through 4, and the LAU1 network. Blue elements indicate negative sign; red elements indicate positive sign. (d) Consistent changes of connection strengths in evolved network populations: colours indicate whether fibre densities increased (red), decreased (blue) or changed in an unspecific direction (green) across 90% or more of the evolved networks belonging to one front.
Mentions: To allow comparisons across datasets, brain networks were down-sampled into a commonly used low-resolution partition of the human cortex, composed of 66 anatomical areas [50], with 33 areas representing the right cortical hemisphere of the brain (see figure 5a). For each dataset, networks evolved towards eight fronts (10 repetitions per front) and the final populations of 500 evolved networks were down-sampled to the low-resolution partition and then aggregated according to front membership. Thus, we obtained eight populations (one for each front) of low-resolution brain networks, each population containing 5000 evolved brain networks. As the four fronts driving networks towards {Ediff < 1} failed to advance, their evolved networks were not investigated further. For the remaining four fronts, we identified anatomical pathways whose fibre density and/or cost has significantly changed during the evolutionary process to favour particular topological traits. For each front, all final populations of evolved networks were aggregated into a single average network, representative of the corresponding front. The differences between the average networks of each front and the corresponding empirical network are shown in figure 5c, together with the corresponding plots recording the consistency with which connections increased or decreased in strength (figure 5d). Each of the fronts is associated with a characteristic pattern of changes in connection weights, and visual inspection suggests greater similarity in the patterns for fronts 1 and 3, and for patterns for fronts 2 and 4, respectively. Analysis of the pairwise cosine angles between average networks of each front confirms this observation, with fronts 1 and 3 (both maximizing CN) and fronts 2 and 4 (both minimizing CN) exhibiting the greatest similarity across all three datasets.Figure 5.

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