Localization and criticality in hierarchical modular networks: Modeling activity patterns in the human brain

Patterns of neural activity in the human brain are characterized by persistent localization phenomena: the brain is able to sustain activity in specific regions for long times and in the absence of external stimuli - a feature which may be essential for explaining the functional differentiation of distinct brain modules. At the same time, the brain is known to give rise to critical behavior: at global scales, activity develops in the form of temporal spikes, called neural avalanches, whose size distribution follows a power law. This aspect may seem in contradiction with the localization picture since critical behavior is, in statistical physics, usually associated with correlations that span an entire system. However this seeming contradiction can be resolved by adopting novel concepts regarding the structure of brain networks. It has been found recently that such networks can be envisaged as hierarchical modular networks (HMNs). If we consider this type of network models, not only localization emerges naturally as a consequence of the network structure, but one also finds that such networks are able to sustain robust critical behavior without the need for fine tuning to a critical point, which would be required to explain criticality in less sophisticated modelling frameworks. Recent mappings of the brain - both structure and activity mappings - are consistent with the idea that the brain can be modeled as a HMN. Starting from this idea, this project aims at a deeper understanding of the relationship between structural features and activity patterns in HMNs, an investigation to which extent similar relationships between network structure and activity patterns can be identified in real structural and functional mappings of the human brain, and a study to which extent they are modified by age or disease. To this end we use the concept of network localization in HMNs and its investigation by spectral analysis, as previously introduced by the applicant. We apply this methodology both to computer generated model brain networks and to experimental data regarding patterns of anatomical connectivity and activity correlation of the human brain. We investigate the following questions: What are the spectral fingerprints of localization in real brain networks, common to both structural and functional mappings? Can a spectral theory of localization in HMNs explain the emergence of such fingerprints? What insights regarding localization and persistence of activity in the human brain and regarding neural avalanche phenomena can we obtain from large-scale computer simulations of empirically supported brain network models?