Metastability in human brain networks: a computational exploration with the Kuramoto model

This thesis delves into metastability in brain networks, a concept that has received a lot of attention in neuroscience due to its capacity to capture the adaptive and flexible dynamics of the brain. The research comprises four main studies and combines methodologies from graph theoretical analysis and dynamics on networks to offer new insights into metastability. The foundation is laid with the introduction of a novel approach for selecting a representative structural group brain network from a set of individuals, the dynamics-based consensus. We posit that the notion of representativeness should extend to dynamics, instead of solely to structure, and we introduce a metric to quantify dynamical representativeness. Shifting focus to structural aspects, we utilise machine learning to predict metastability based on structural metrics. Feature importance helps us narrow down crucial structural features, corroborating findings in the literature about the impact of global measures like modularity, but also shedding light on the capacity of nodal features such as betweenness centrality to predict metastability. We follow with an investigation that utilises a systematic and convergent series of null network models, to dissect out the structural features that are most determinant of the metastable dynamics of the network. It is shown that retaining the degree distribution, degree correlations and clustering are sufficient to capture metastable behaviour. Finally, we investigate the functional implications of differences in metastability with a perturbational study that explores the link between metastability and the critical transition. By perturbing the dynamics-based consensus, it is revealed that metastability can predict the magnitude of the response to perturbations, and the metastability peak coincides with the maximum perturbation response. This work shows that the maximum of metastability indeed marks the critical transition, and highlights a functional implication of network metastability (namely, its predictive capacity for perturbation sensitivity). Future studies could validate these findings in weighted networks or models tuned to empirical data.