Data-driven inference of brain dynamical states from the r-spectrum of correlation matrices

TL;DR

This paper introduces a data-driven method to characterize individual brain dynamical states from correlation matrices using a percolation-based threshold, providing stable, interpretable measures that relate to known neural dynamics.

Contribution

The study develops a novel correlation thresholding approach that identifies a characteristic percolation point, enabling physically meaningful comparisons of brain states across individuals.

Findings

The method produces stable, subject-specific dynamical state estimates.

The percolation threshold correlates with established neural indicators.

Simulations confirm the method tracks changes in collective brain dynamics.

Abstract

We present a data-driven framework to characterize large-scale brain dynamical states directly from correlation matrices at the single-subject level. By treating correlation thresholding as a percolation-like probe of connectivity, the approach tracks multiple cluster- and network-level observables and identifies a characteristic percolation threshold, rc, at which these signatures converge. We use $r_c$ as an operational and physically interpretable descriptor of large-scale brain dynamical state. Applied to resting-state fMRI data from a large cohort of healthy individuals (N = 996), the method yields stable, subject-specific estimates that covary systematically with established dynamical indicators such as temporal autocorrelations. Numerical simulations of a whole-brain model with a known critical regime further show that $r_c$ tracks changes in collective dynamics under controlled variations of excitability. By replacing arbitrary threshold selection with a criterion intrinsic to correlation structure, the r-spectra provides a physically grounded approach for comparing brain dynamical states across individuals.