Brain Network Dynamics Adhere to a Power Law

Dardo G. Tomasi, Ehsan Shokri-Kojori, Nora D. Volkow

The temporal dynamics of complex networks such as the Internet are characterized by a power scaling between the temporal mean and dispersion of signals at each network node. Here we tested the hypothesis that the temporal dynamics of the brain networks are characterized by a similar power law. This realization could be useful to assess the effects of randomness and external modulators on the brain network dynamics. Simulated data using a well-stablished random diffusion model allowed us to predict that the temporal dispersion of the amplitude of low frequency fluctuations (ALFF) and that of the local functional connectivity density (lFCD) scale with their temporal means. We tested this hypothesis in open-access resting-state functional magnetic resonance imaging datasets from 66 healthy subjects. A robust power law emerged from the temporal dynamics of ALFF and lFCD metrics, which was insensitive to the methods used for the computation of the metrics. The scaling exponents (ALFF: 0.8 ± 0.1; lFCD: 1.1 ± 0.1; mean ± SD) decreased with age and varied significantly across brain regions; multimodal cortical areas exhibited lower scaling exponents, consistent with a stronger influence of external inputs, than limbic and subcortical regions, which exhibited higher scaling exponents, consistent with a stronger influence of internal randomness. Findings are consistent with the notion that external inputs govern neuronal communication in the brain and that their relative influence differs between brain regions. Further studies will assess the potential of this metric as biomarker to characterize neuropathology.