Topological Network Analysis of Electroencephalographic Power Maps

Abstract

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.

A survey of brain network analysis by electroencephalographic signals

“…The brain network topology changes adaptively and tempospatially (Jirsa et al 2010) when responding to a certain environment or factor. This is called neuroplasticity of the brain, and this phenomenon is called reconfiguration or reorganization which needs to update the ongoing network connectivity with transient and heterogeneous (various) connections from resting-state or default mode network (DMN) connectivity (de Oliveira 2020; Wang et al 2017).…”

Topological Distances Between Brain Networks

“…Developing efficient algorithms for handling higher dimensional Delaunay complex is a subject of ongoing research (Boissonnat et al, 2009a). Wang et al (2017b) used the Delaunay triangulation in building a complex from EEG channel locations.…”

“…Instead of doing graph filtration at the edge level, it is possible to build different kind of filtrations at the node level (Hofer et al, 2020;Wang et al, 2017b). Consider graph G = (V, E) with nodes V = 1, 2, • • • , p and node weights w i defined at each node i.…”

“…In Wang et al (2018), persistent homology using the persistent landscape was shown to outperform power spectral density and local variance methods. In Wang et al (2017b), persistent homology was shown to outperform topographic power maps. In Yoo et al (2017), center persistency was shown to outperform the network-based statistic and element-wise multiple corrections.…”

Local Sleep Slow-Wave Activity Colocalizes With the Ictal Symptomatogenic Zone in a Patient With Reflex Epilepsy: A High-Density EEG Study

“…''Scalp level'', as utilized in this manuscript, refers to the topographic mapping of SWA (Nuwer, 1988). This approach provides a two-dimensional rendering of brain activity (Wang et al, 2017). ''Source space'' or ''source reconstruction'' analysis combined these data with a forward model and minimum norm plus smoothness priors to provide a three-dimensional location of SWA changes on the cortical surface (López et al, 2014;Michel and Brunet, 2019).…”