Pattern dynamics and stochasticity of the brain rhythms

We adopt recently introduced mathematical concepts of pattern stochasticity to quantifying transient behavior of extracellular fields at "temporal mesoscale." Currently, the mean extracellular fields (or any biological signals for that matter) are analyzed based either on their instantaneous parameters, agnostic of protracted behaviors, or time-averaged characteristics, which highlight mean trends. What remains unexplored, is the actual structure of waves—their shapes and patterns over finite timescales. We offer a methodology that is sensitive to individual, time localized features and yet allows describing a given waveform as a single entity, without defeaturing, putting each pattern, as a whole, into a statistical perspective. This approach allows attributing precise meaning to commonly used intuitive notions such as a brain wave's "regularity," "typicality," or "orderliness," and affords distinguishing statistically mundane wave patterns from atypical ones (e.g., atypically periodic or excessively time-cluttering) as well as capturing transitions between them. Applying these analyses to local field potentials recorded in mice hippocampi and correlating wave-pattern dynamics with changes in the animals' motor activity, we demonstrate motion-modulated changes of the wave's cadence, an antiphase relationship between orderliness and acceleration, spatial selectiveness of patterns, coupling to the animals' attention and other behavioral parameters. These results offer a complementary—morphological—description of the brain waves' structure, dynamics, and functionality, providing a novel perspective om neuronal circuits' dynamics and functionality.