Dynamic Topological Data Analysis of Functional Human Brain Networks

TL;DR

This paper introduces a novel dynamic topological data analysis framework that captures the evolving topology of brain networks over time, enabling discrimination of different brain states and gender differences in functional MRI data.

Contribution

The paper presents a new dynamic-TDA method that constructs persistent homology over time series of brain networks, extending static TDA to analyze dynamic brain activity.

Findings

Successfully discriminates between male and female brain network topologies.

Applies to resting-state fMRI data, demonstrating practical utility.

Provides MATLAB code for reproducibility.

Abstract

Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology, can handle such a challenge. However, existing TDA has been somewhat limited to capturing the static summary of dynamically changing brain networks. We propose a novel dynamic-TDA framework that builds persistent homology over a time series of brain networks. We construct a Wasserstein distance based inference procedure to discriminate between time series of networks. The method is applied to the resting-state functional magnetic resonance images of human brain. We demonstrate that our proposed dynamic-TDA approach can distinctly discriminate between the topological patterns of male and female brain networks. MATLAB code for implementing this method is available at https://github.com/laplcebeltrami/PH-STAT.