The temporal structures and functional significance of scale-free brain activity

Scale-free dynamics, with a power spectrum following P proportional to f(-beta), are an intrinsic feature of many complex processes in nature. In neural systems, scale-free activity is often neglected in electrophysiological research. Here, we investigate scale-free dynamics in human brain and show that it contains extensive nested frequencies, with the phase of lower frequencies modulating the amplitude of higher frequencies in an upward progression across the frequency spectrum. The functional significance of scale-free brain activity is indicated by task performance modulation and regional variation, with beta being larger in default network and visual cortex and smaller in hippocampus and cerebellum. The precise patterns of nested frequencies in the brain differ from other scale-free dynamics in nature, such as earth seismic waves and stock market fluctuations, suggesting system-specific generative mechanisms. Our findings reveal robust temporal structures and behavioral significance of scale-free brain activity and should motivate future study on its physiological mechanisms and cognitive implications.