Topological Network Analysis of Electroencephalographic Power Maps.

Meditation practice as a non-pharmacological intervention to provide health related benefits has generated much neuroscientific interest in its effects on brain activity. Electroencephalogram (EEG), an imaging modality known for its inexpensive procedure and excellent temporal resolution, is often utilized to investigate the neuroplastic effects of meditation under various experimental conditions. In these studies, EEG signals are routinely mapped on a topographic layout of channels to visualize variations in spectral powers within certain frequency ranges. Topological data analysis (TDA) of the topographic power maps modeled as graphs can provide different insight to EEG signals than standard statistical methods. A highly effective TDA technique is persistent homology, which reveals topological characteristics of a power map by tracking feature changes throughout a filtration process on the graph structure of the map. In this paper, we propose a novel inference procedure based on filtrations induced by sublevel sets of the power maps of high-density EEG signals. We apply the pipeline to simulated and real data, where we compare the persistent homological features of topographic maps of spectral powers in high-frequency bands of EEG signals recorded on long-term meditators and meditation-naive practitioners.