Optimal hierarchical modular topologies for producing limited sustained activation of neural networks

Marcus Kaiser

doi:10.3389/fninf.2010.00008

Abstract

An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable regimes of network activation, typically arising from a limited parameter range. In this range of limited sustained activity (LSA), the activity of neural populations in the network persists between the extremes of either quickly dying out or activating the whole network. Hierarchical modular networks were previously found to show a wider parameter range for LSA than random or small-world networks not possessing hierarchical organization or multiple modules. Here we explored how variation in the number of hierarchical levels and modules per level influenced network dynamics and occurrence of LSA. We tested hierarchical configurations of different network sizes, approximating the large-scale networks linking cortical columns in one hemisphere of the rat, cat, or macaque monkey brain. Scaling of the network size affected the number of hierarchical levels and modules in the optimal networks, also depending on whether global edge density or the numbers of connections per node were kept constant. For constant edge density, only few network configurations, possessing an intermediate number of levels and a large number of modules, led to a large range of LSA independent of brain size. For a constant number of node connections, there was a trend for optimal configurations in larger-size networks to possess a larger number of hierarchical levels or more modules. These results may help to explain the trend to greater network complexity apparent in larger brains and may indicate that this complexity is required for maintaining stable levels of neural activation.

Highlights

Complex systems operate within a critical functional range (Bak et al, 1987), sustaining diverse dynamical states on the basis of their intricate system architecture
This study investigated an essential precondition of criticality in neural systems, the capability of neural networks to produce limited sustained activity (LSA) patterns following an initial activation
We addressed this question by simulating the spreading of neural activity and systematically varying model parameters and network topology in hierarchical modular networks, which are inspired by the organization of biological neural networks across scales

Summary

Introduction

Complex systems operate within a critical functional range (Bak et al, 1987), sustaining diverse dynamical states on the basis of their intricate system architecture. Recent studies indicate that brain networks operate close to a critical point Evidence for this comes, for example, from the observation of neuronal avalanches (i.e., bursts of activity separated by longer periods of relative rest) with a power-law size distribution in cortical slices (Beggs and Plenz, 2003), and from time series analysis of EEG data (Freeman et al, 2000) showing that the power spectral density of background activity follows a power law. While its functional significance is still not well understood, it has been suggested that critical dynamics may enhance information processing capabilities of neuronal networks (e.g., Bertschinger and Natschläger, 2004) This idea is supported by work showing that the dynamic range in an excitable network is optimized at criticality (Kinouchi and Copelli, 2006). It is desirable to obtain a better understanding of the conditions for criticality in complex excitable networks

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Conclusion