Parabolic avalanche scaling in the organization of complex brain functions*

Complex brain functions are underpinned by the organized activities of large groups of nerve cells, particularly in the brain's cortex, a region that has significantly evolved in mammals. Despite its evolutionary importance, the operational principles of the cortex remain elusive. A key feature of cortical activity involves 'neuronal avalanches,' where excitatory nerve cells trigger cascading activities indicative of critical dynamics. Although such avalanches are a recognized phenomenon in various mammals, including humans, their specific characteristics in terms of size and duration were not fully understood. Our latest research with non-human primates and rodents demonstrates that these neuronal avalanches exhibit a scale-invariant growth in relation to their duration. This finding aligns with critical dynamics predictions and is supported by simulations of networks balancing excitation and inhibition. We found that these avalanches follow a parabolic pattern over time, lasting up to 5 seconds and spanning extensive cortical areas. These parabolic patterns maximize the complexity of neuronal activities, both in restful wakefulness and in response to sensory stimulation. Our study thus reveals a consistent, scale-invariant pattern in cortical activity, crucial for complex brain functions.