Turbulence in the human brain: Discovering the homogeneous isotropic functional core organisation of the human brain

Turbulence is a special dynamical state driving many physical systems by way of its ability to facilitate fast energy/information transfer across scales. These qualities are important for brain function, but it is currently unknown if the brain also exhibits turbulence as a fundamental organisational principle. Using large-scale neuroimaging data from 1003 healthy participants, we demonstrate both empirically and through the use of a computational whole-brain model that human brain dynamics is organised around a turbulent homogeneous isotropic functional core. We show the economy of anatomy of this functional core following the exponential Markov-Kennedy distance rule of anatomical connections as a cost-of-wiring principle, which displays a turbulent-like power scaling law for functional correlations in a broad spatial range suggestive of a cascade of information processing. Further investigating this, we use the theory of turbulence in coupled oscillators in a whole-brain model to demonstrate that the best fit of our model to the data corresponds to a region of maximally developed amplitude turbulence, which also corresponds to maximal sensitivity to the processing of external stimulations (information capability). This establishes a firm link between turbulence and optimal brain function. Finally, we investigate the contrast between resting and seven tasks, and find the turbulent core in task is similar to that resting state but that the long-distance correlations show task-specific increases. These controlling, symmetry-breaking regions are found in higher-order brain regions outside primary sensory regions. Overall, our results reveal a novel way of analysing and modelling whole-brain dynamics that for the first time ever establishes turbulence as a fundamental basic principle of brain organisation.