Turbulent-like dynamics in the human brain

Abstract

Using large-scale neuroimaging data from 1003 healthy participants, we demonstrate empirically and theoretically that human brain dynamics is organised around a homogeneous isotropic functional core. More importantly, this homogeneous isotropic functional core follows a turbulentlike power scaling law for functional correlations in a broad spatial range suggestive of a cascade of information processing. The underlying anatomy of the brain is expensive in terms of material and metabolic costs and it has been suggested that the trade-offs between wiring cost and topological value change over many timescales but exactly how is not known (1). Here, we demonstrate how the economy of anatomy has evolved a homogeneous isotropic functional core by using wholebrain modelling with the exponential Markov-Kennedy distance rule of anatomical connections as the cost-of-wiring principle demonstrated in the massive retrograde tract tracing studies in nonhuman primates by Markov, Kennedy and colleagues (2). Overall, our results reveal a novel way of analysing and modelling whole-brain dynamics that establishes a fundamental basic principle of brain organisation.

Rare long-range cortical connections enhance information processing

“…In fact, fitting the functional neuroimaging data with λ ? as a free parameter yielded values lower than the one estimated here from the structural data 15 . Nevertheless, for consistency we use the latter here.…”

“…Unlike the results in mice and non-human primates, the estimate found here is based on dMRI tractography and may be overestimating the λ s , which is likely to be smaller. In fact, fitting the functional neuroimaging data with λ s as a free parameter yielded values lower than the one estimated here from the structural data 15 . Nevertheless, for consistency we use the latter here.…”

“…Except for a very recent study 15 , amplitude turbulence has been studied exclusively in the supercritical regime of the Stuart-Landau coupled oscillators 8, 9 . Yet, given that a range of papers have demonstrated that the Stuart-Landau oscillators fit the neuroimaging brain data when used in the subcritical regime at the edge of the bifurcation 14, 16-18 , it was recently demonstrated to fit the functional MRI data from 1003 participants and to exhibit amplitude turbulence as characterised by Equation 2 15 . The subcritical regime at the edge of the bifurcation is not showing deterministic spatiotemporal chaos in the way found in under the supercritical regime but rather some very interesting state dynamics, perhaps best described as turbulent-like or turbulent fluctuation, which are described by Equation 2.…”

“…The subcritical regime at the edge of the bifurcation is not showing deterministic spatiotemporal chaos in the way found in under the supercritical regime but rather some very interesting state dynamics, perhaps best described as turbulent-like or turbulent fluctuation, which are described by Equation 2. Interestingly, in the supercritical regime, turbulence is directly linked to the shear parameter of the Stuart-Landau equation, which is not needed for the subcritical regime at the brink of the bifurcation 15 and thus is not included here.…”

“…Research has investigated the hierarchical organisation of brain structure and function [31][32][33][34] , which has demonstrated a common network available for the orchestration of task and rest 15 . Previous research has demonstrated that the turbulent core of brain activity is largely overlapping with brain regions known to be involved in lower level sensory processing 15 . We therefore hypothesise that the anatomical basis of this orchestration could be well served by the long-range outliers, which effectively are able to control brain activity in the turbulent core sustained by the underlying EDR.…”