Spatiotemporal Patterns of Adaptation-Induced Slow Oscillations in a Whole-Brain Model of Slow-Wave Sleep

During slow-wave sleep, the brain is in a self-organized regime in which slow oscillations (SOs) between up- and down-states travel across the cortex. While an isolated piece of cortex can produce SOs, the brain-wide propagation of these oscillations are thought to be mediated by the long-range axonal connections. We address the mechanism of how SOs emerge and recruit large parts of the brain using a whole-brain model constructed from empirical connectivity data in which SOs are induced independently in each brain area by a local adaptation mechanism. Using an evolutionary optimization approach, good fits to human resting-state fMRI data and sleep EEG data are found at values of the adaptation strength close to a bifurcation where the model produces a balance between local and global SOs with realistic spatiotemporal statistics. Local oscillations are more frequent, last shorter, and have a lower amplitude. Global oscillations spread as waves of silence across the undirected brain graph, traveling from anterior to posterior regions. These traveling waves are caused by heterogeneities in the brain network in which the connection strengths between brain areas determine which areas transition to a down-state first, and thus initiate traveling waves across the cortex. Our results demonstrate the utility of whole-brain models for explaining the origin of large-scale cortical oscillations and how they are shaped by the connectome.

Propofol anesthesia alters cortical traveling waves

Oscillatory dynamics in cortex seem to organize into traveling waves that serve a variety of functions. Recent studies show that propofol, a widely used anesthetic, dramatically alters cortical oscillations by increasing slow-delta oscillatory power and coherence. It is not known how this affects traveling waves. We compared traveling waves across the cortex of non-human primates (NHPs) before, during, and after propofol-induced loss-of-consciousness (LOC). After LOC, traveling waves in the slow-delta (~ 1Hz) range increased, grew more organized, and travelled in different directions relative to the awake state. Higher frequency (8-30 Hz) traveling waves, by contrast, decreased, lost structure, and switched to directions where the slow-delta waves were less frequent. The results suggest that LOC may be due, in part, to changes in slow-delta traveling waves that, in turn, alter and disrupt traveling waves in the higher frequencies associated with cognition.

Cortical traveling waves reflect state-dependent hierarchical sequencing of local regions in the human connectome network

Recent human studies using electrocorticography have demonstrated that alpha and theta band oscillations form traveling waves on the cortical surface. According to neural synchronization theories, the cortical traveling waves may group local cortical regions and sequence them by phase synchronization; however these contributions have not yet been assessed. This study aimed to evaluate the functional contributions of traveling waves using connectome-based network modeling. In the simulation, we observed stable traveling waves on the entire cortical surface wherein the topographical pattern of these phases was substantially correlated with the empirically obtained resting-state networks, and local radial waves also appeared within the size of the empirical networks (< 50 mm). Importantly, individual regions in the entire network were instantaneously sequenced by their internal frequencies, and regions with higher intrinsic frequency were seen in the earlier phases of the traveling waves. Based on the communication-through-coherence theory, this phase configuration produced a hierarchical organization of each region by unidirectional communication between the arbitrarily paired regions. In conclusion, cortical traveling waves reflect the intrinsic frequency-dependent hierarchical sequencing of local regions, global traveling waves sequence the set of large-scale cortical networks, and local traveling waves sequence local regions within individual cortical networks.

Stability of Traveling Waves to a Burgers Equation with 2nd-Order Nonlinear Diffusion

We are interested in the study of asymptotic stability for Burgers equation with second-order nonlinear diffusion. We first transform the original equation by the ansatz transformation to establish the existence of traveling wave. We further employ the energy estimate under small perturbation and arbitrary wave amplitude. This energy estimate is then used to establish the stability.