Complex harmonics reveal low-dimensional manifolds of critical brain dynamics

Abstract

The brain needs to perform time-critical computations to ensure survival. A potential solution lies in the nonlocal, distributed computation at the whole-brain level made possible by criticality and amplified by the rare long-range connections found in the brain's unique anatomical structure. This nonlocality can be captured by the mathematical structure of Schrödinger's wave equation, which is at the heart of the complex harmonics decomposition (CHARM) framework that performs the necessary dimensional manifold reduction able to extract nonlocality in critical spacetime brain dynamics. Using a large neuroimaging dataset of over 1000 people, CHARM captured the critical, nonlocal and long-range nature of brain dynamics and the underlying mechanisms were established using a precise whole-brain model. Equally, CHARM revealed the significantly different critical dynamics of wakefulness and sleep. Overall, CHARM is a promising theoretical framework for capturing the low-dimensionality of the complex network dynamics observed in neuroscience and provides evidence that networks of brain regions rather than individual brain regions are the key computational engines of critical brain dynamics.

G.D. is supported by Grant PID2022-136216NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by 'ERDF A way of making Europe', ERDF, EU, Project NEurological MEchanismS of Injury, and Sleeplike cellular dynamics (NEMESIS) (ref. 101071900) funded by the EU ERC Synergy Horizon Europe, and AGAUR research support grant (ref. 2021 SGR 00917) funded by the Department of Research and Universities of the Generalitat of Catalunya. Y.S.P. is supported by the project NEurological MEchanismS of Injury, and Sleep-like cellular dynamics (NEMESIS) (ref. 101071900) funded by the EU ERC Synergy Horizon Europe. M.L.K. is supported by the Centre for Eudaimonia and Human Flourishing (funded by the Pettit and Carlsberg Foundations) and Center for Music in the Brain (funded by the Danish National Research Foundation, DNRF117).