UC San Diego

Electroencephalography (EEG) is a fundamental technique for studying and understanding the brain through its electrical oscillations. Within this field, the phenomena where the phase of slow brain rhythm modulates a faster rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining attention due to its occurrence in normal and pathological brain processes in humans and across different mammalian species. In the quest to understand PAC's physiological role in the brain, the development of signal processing methods and software supporting its study is key for further advancement. Several methods have been proposed to estimate a measure of the PAC process, but only a few have addressed its temporal dynamics. Furthermore, it appears that no studies have addressed PAC dynamics while assuming its possible directional delay characteristics. \par

This dissertation's goal is twofold: to provide new methods to estimate and characterize PAC dynamics, and to provide dedicated software with high-performance computing (HPC) support for computing PAC in electrophysiological signals from the brain. \par

Here I first propose and validate a mutual information-based method for computing time-resolved PAC, MIPAC. Then, I characterize and lay out the foundations for using a novel directed information theory measure, transfer entropy, to study delayed interactions from the phase to amplitude components in the PAC process. Following, I propose a new EEGLAB plug-in toolbox, PACTools, that allows computing PAC in either continuous or event-related EEG data using multiple currently available methods, including the newly developed MIPAC. PACTools operate seamlessly with EEGLAB, and features built-in access to free HPC resources at the Neurosciences Gateway (\textit{nsgportal.org)}. This feature is possible by developing another EEGLAB plug-in I'm introducing here, nsgportal, that interfaces EEGLAB with NSG directly from within EEGLAB on any personal computer. The tools and methods presented in this dissertation constitute a comprehensive framework aiming at facilitating the study of the PAC's role in the healthy and pathological brain.