Non-local Schrödinger diffusion model reveals mechanisms of critical brain dynamics

Abstract

Time-efficient computation is essential for survival. It has been proposed that this is made possible through the principle of criticality amplified by the rare long-range connections found in the brain's unique anatomical structure, which together provide the necessary non-local, distributed computation. Here, we directly tested this hypothesis by building a non-local, diffusion whole-brain model using the mathematical structure of Schrödinger's equation to capture non-local/long-range brain dynamics. We tested this non-local diffusion model against a conventional state-of-the-art local diffusion model in large-scale empirical neuroimaging data from over 1,000 healthy human participants and found the non-local model performed significantly better at capturing the brain dynamics. Overall, these results demonstrate that the non-locality of Schrödinger's equation is excellent for revealing the necessary non-local (but non-quantum) properties of the human brain.

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 Sleep-like 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 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).