Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia

TL;DR

This study applies topological data analysis, specifically persistent homology, to fMRI brain networks from schizophrenia patients, healthy controls, and siblings, revealing distinct topological features that differentiate these groups.

Contribution

It introduces a novel application of persistent homology to task-based fMRI data, uncovering topological biomarkers for schizophrenia and related groups.

Findings

Sibling cohort shows unique 1-dimensional loop features.

Persistence images distinguish all three groups.

Identified brain regions involved in topological differences.

Abstract

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions.