UC San Diego

The brain endogenously generates electrical activity that arises from the complex, nonlinear interactions of its components. During sleep, large amplitude, slow oscillations as well as 10-16 Hz rhythms known as sleep spindles are generated in the cortex and thalamus respectively, and their coupling has been shown to bolster our memory capacities by facilitating cortical plasticity. Identifying where particular sleep rhythms are generated, how they co-occur with other regions, and whether rhythms differ in frequency or other characteristics can inform mechanisms for how they coordinate information exchange during sleep. In this dissertation, I characterized the cortical and thalamic activity of sleep spindles, theta bursts (~6 Hz), a novel sleep rhythm identified here, and the coupling of spindles and theta bursts with slow waves using intracranial recordings from epileptic patients. I also report regional differences in spindle properties, largely inaccessible to non-invasive recordings, that propose a modified view of spindle dynamics across the cortex. The most common characterizations of brain dynamics, including the sleep rhythms reported here, are largely based on linear time-frequency analyses. However, because the brain is a high-dimensional, nonlinear system, applying linear techniques alone may not sufficiently capture the relevant dynamical features. To address this, I helped develop nonlinear tools, based on Delay Differential Analysis (DDA), for analyzing neural time series. I evaluated these tools in simulated, chaotic systems, which are suitable models for recurrent, continuous, and nonlinear dynamics. Specifically, I investigated whether given a set of recorded time series, can we (1) assess whether two signals are causally interacting and (2) rank signals by their amount of dynamical information about the original system. These applications of DDA, in tandem with traditional linear techniques, can improve our understanding of underlying brain activity during seizures and sleep. In Chapter 1, I characterize a novel sleep rhythm, the theta burst, that is distinct from sleep spindles, recorded in both the cortex and thalamus, and which in both structures, precedes downstates. In Chapter 2, I report distinct sources of spindle variability, including variability across channels within a region, across spindles within a single recording site, and across cycles within a spindle, and how these sources are of a size comparable to the frontal-parietal difference typically used to summarize spindle dynamics. Chapter 3 introduces a novel nonlinear signal processing technique, Cross-Dynamical Delay Differential Analysis (CD-DDA), for inferring causal interactions between time series and applies this approach to track seizure spread in a patient with epilepsy. Chapter 4 applies DDA in simulated chaotic dynamical systems to assess the observability of a time series, i.e. how much dynamical information a variable has about the original system it is a part of.