Physics (Internal)

Critical Dynamics and Self-organization in Bursts of Brain Rhythms as a Fundamental Hallmark of Physiological Function

This event is part of the Preliminary Oral Exam.

Examining Committee: Plamen Ivanov, Karl Ludwig, Shyam Erramilli, Kirill Korolev

Abstract: In nature, systems consisting of many interacting constituents may organize themselves into a state characteristic of equilibrium systems at the critical point, without any significant external "tuning". The dynamics of such systems is characterized by long-range spatio-temporal correlations, and the statistical properties are described by power-laws. Following Bak, Tang and Wiesenfeld, this behavior is described as self-organized criticality (SOC). In the mammalian brain, neuronal networks exhibit bursting dynamics, with a complex temporal organization that involves rhythms covering a broad range of frequencies. Rhythms in different frequency bands often occur in bursts that last from seconds to minutes, and are one of the most important features of brain activity throughout the entire sleep-wake cycle. Earlier studies have reported that the micro-structure of wake and sleep episodes shows a SOC-like dynamics. Based on these earlier observations, we initiated investigations of the bursting dynamics of θ and δ rhythms, which are typically associated with sleep. We found that bursts of θ rhythms exhibit a temporal organization characterized by a power-law probability distribution for their durations and long-range power-law correlations. In contrast, δ-burst durations follow a Weibull distribution, rather than a power-law. These distinct behaviors of θ- and δ-bursts are reminiscent of the ‘avalanche’ and waiting time dynamics in other out-of-equilibrium physical systems exhibiting SOC, and in their corresponding models. We find that the duality of power-law vs Weibull and the associated scaling properties are robust features of brain dynamics across the sleep-wake cycle. Moreover, in addition to the long-range power-law temporal correlations in the bursting dynamics of θ and δ-bursts, we uncover a robust coupling between the durations of consecutive θ and δ bursts. The discovered non-equilibrium features in brain dynamics fall outside the current paradigm of sleep as a system in equilibrium (homeostasis), are not addressed by current empirical and modeling investigations, and open new avenues to understanding brain dynamics and functions under healthy conditions and pathological perturbations.