Sustained activity in hierarchical modular neural networks: self-organized criticality and oscillations

Wang Wang

doi:10.3389/fncom.2011.00030

Abstract

Cerebral cortical brain networks possess a number of conspicuous features of structure and dynamics. First, these networks have an intricate, non-random organization. In particular, they are structured in a hierarchical modular fashion, from large-scale regions of the whole brain, via cortical areas and area subcompartments organized as structural and functional maps to cortical columns, and finally circuits made up of individual neurons. Second, the networks display self-organized sustained activity, which is persistent in the absence of external stimuli. At the systems level, such activity is characterized by complex rhythmical oscillations over a broadband background, while at the cellular level, neuronal discharges have been observed to display avalanches, indicating that cortical networks are at the state of self-organized criticality (SOC). We explored the relationship between hierarchical neural network organization and sustained dynamics using large-scale network modeling. Previously, it was shown that sparse random networks with balanced excitation and inhibition can sustain neural activity without external stimulation. We found that a hierarchical modular architecture can generate sustained activity better than random networks. Moreover, the system can simultaneously support rhythmical oscillations and SOC, which are not present in the respective random networks. The mechanism underlying the sustained activity is that each dense module cannot sustain activity on its own, but displays SOC in the presence of weak perturbations. Therefore, the hierarchical modular networks provide the coupling among subsystems with SOC. These results imply that the hierarchical modular architecture of cortical networks plays an important role in shaping the ongoing spontaneous activity of the brain, potentially allowing the system to take advantage of both the sensitivity of critical states and the predictability and timing of oscillations for efficient information processing.

Highlights

The impact of network topology on the dynamical behavior of network systems is a topic of central importance for the understanding of complex systems, and has attracted much attention in the complex network field (Strogatz, 2001); Albert and Barabási, 2002; Boccaletti et al, 2006; Arenas et al, 2008)
Network activations were simulated by providing each node with background noise activation for 200 ms, and removing the noise to check whether the networks could sustain the activity on their own
These results show that both criticality and low-frequency oscillations are quite robust when hierarchical modular network (HMN) are embedded in more complex realistic cortical networks, implying that the combination of the hierarchical modular architecture and the balance of excitation with inhibition may generally play an important role in the activity of the brain

Summary

Introduction

The impact of network topology on the dynamical behavior of network systems is a topic of central importance for the understanding of complex systems, and has attracted much attention in the complex network field (Strogatz, 2001); Albert and Barabási, 2002; Boccaletti et al, 2006; Arenas et al, 2008). One prominent feature of this organization is modularity It is known from the anatomy of the brain that cortical architecture is organized in a hierarchical and modular way, from cellular micro-circuits in cortical columns at the lowest level, via cortical areas at the intermediate level, to sets of highly connected brain regions at the global systems level (Mountcastle, 1997; Hilgetag et al, 2000; Hilgetag and Kaiser, 2004). This means that neurons within a column, an area or a set of areas are more densely linked with each other than with neurons in the rest of the network (Hilgetag et al, 2000; Hilgetag and Kaiser, 2004; Sporns et al, 2004; Kaiser et al, 2007), resulting in the multi-scale organization of a hierarchical modular network (HMN)

Results

Discussion

Conclusion