Persistent Homological State-Space Estimation of Functional Human Brain Networks at Rest

The paper introduces a new data-driven topological data analysis (TDA) method for studying dynamically changing human functional brain networks obtained from the resting-state functional magnetic resonance imaging (rs-fMRI). Leveraging persistent homology, a multiscale topological approach, we present a framework that incorporates the temporal dimension of brain network data. This allows for a more robust estimation of the topological features of dynamic brain networks. The method employs the Wasserstein distance to measure the topological differences between networks and demonstrates greater efficiency and performance than the commonly used -means clustering in defining the state spaces of dynamic brain networks. Our method maintains robust performance across different scales and is especially suited for dynamic brain networks. In addition to the methodological advancement, the paper applies the proposed technique to analyze the heritability of overall brain network topology using a twin study design. The study investigates whether the dynamic pattern of brain networks is a genetically influenced trait, an area previously underexplored. By examining the state change patterns in twin brain networks, we make significant strides in understanding the genetic factors underlying dynamic brain network features. Furthermore, the paper makes its method accessible by providing MATLAB codes, contributing to reproducibility and broader application.