Single region contribution to the brain dynamic (in)stability

An open question in neuroscience regards the origin of the flexible and heterogeneous spatio-temporal patterns of neural correlations assessed with fMRI. Model-based approaches are commonly used to shed light on this problem with the aim to reproduce the same dynamical richness observed in the empirical recordings. In particular, dynamic causal models are generative top-down models commonly used in this field based on a state-space representation where the state refers to the hidden neural dynamic. The corresponding state matrix is the so-called effective connectivity that is interpreted as a representation of the causal interactions between each ordered brain region pair. By looking at the effective connectivity in the context of linear system theory, we can derive a rich characterization of the dynamics of the system. In this work we propose a method for studying how each brain region participate in defining the global stability of the system and its application to both mouse and human resting-state fMRI datasets. In detail, this analysis is based on a decomposition of the state matrix into two components: a dissipative symmetric gradient flow, and a solenoidal component which accounts for the asymmetric, i.e. directional, coupling. By acting on the solenoidal part, we can simulate the segregation of a single region and evaluate its effect on the eigenvalues of the state matrix, specifically those related to the slower dynamics.