Topological Data Analysis of Electroencephalogram Signals for Pediatric Obstructive Sleep Apnea

TL;DR

This work addresses noninvasive pediatric OSA diagnosis by distinguishing OSA+ from OSA− using EEG-derived brain connectivity analyzed with Topological Data Analysis. The authors build distance matrices from smoothed periodograms and coherence across 7 EEG channels, construct a Rips filtration via Ripser.py, and summarize topological features as persistence landscapes focused on $H_0$; a permutation test with $B=1000$ assesses group differences. An extensive pediatric dataset from the NCH Sleep DataBank demonstrates statistically significant differences (p<0.05) across all sleep stages (NREM1, NREM2, NREM3, REM) and all bands (Delta to Gamma). The results lay a foundation for cohort-level OSA classification and point toward a future where a single EEG could assist diagnosis, with further work needed to translate these findings into clinical utility and to relate TDA features to respiration-based measures.

Abstract

Topological data analysis (TDA) is an emerging technique for biological signal processing. TDA leverages the invariant topological features of signals in a metric space for robust analysis of signals even in the presence of noise. In this paper, we leverage TDA on brain connectivity networks derived from electroencephalogram (EEG) signals to identify statistical differences between pediatric patients with obstructive sleep apnea (OSA) and pediatric patients without OSA. We leverage a large corpus of data, and show that TDA enables us to see a statistical difference between the brain dynamics of the two groups.

Figures (2)

• Figure 1: Example Persistence Diagram for Delta Band of an OSA Positive Patient
• Figure 2: Example Degree 0 Persistence Landscape for Delta Band of an OSA Positive Patient

Theorems & Definitions (2)

• Definition III.1: Simplicial Complex edelsbrunnerComputationalTopologyIntroduction2010
• Definition III.2: Simplicial Homology Group chazalIntroductionTopologicalData2021b