Multistability in Large Scale Models of Brain Activity

Noise driven exploration of a brain network’s dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network’s capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain’s dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system’s attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the “resting state” condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.Author Summary: Recent developments in non-invasive brain imaging allow reconstructing axonal tracts in the human brain and building realistic network models of the human brain. These models resemble brain systems in their network character and allow deciphering how different regions share signals and process information. Inspired by the metastable dynamics of the spin glass model in statistical physics, we systematically explore the brain network’s capacity to process information and investigate novel avenues how to enhance it. In particular, we study how the brain activates and switches between different functional networks across time. Such non-stationary behavior has been observed in human brain imaging data and hypothesized to be linked to information processsing. To shed light on the conditions under which large-scale brain network models exhibit such dynamics, we characterize the principal network patterns and confront them with modular structures observed both in graph theoretical analysis and resting-state functional Magnetic Resonance Imaging (rs-fMRI).