Topological data analysis of task-based fMRI data from experiments on schizophrenia

Bernadette J Stolz,Satu Nahkuri,Mason A Porter,Heather A Harrington,Tegan Emerson

doi:10.1088/2632-072x/abb4c6

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 functional magnetic resonance imaging (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 of 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 represent the output of our persistent-homology calculations, and we study the persistence landscapes and persistence 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 one-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.

Highlights

Schizophrenia is a chronic psychiatric disorder that affects more than 21 million people worldwide [1]
One can form a so-called functional network [10, 11, 18,19,20], in which each node represents a brain region and one weights the edges between them based on some measure of the similarity between the nodes’ functional magnetic resonance imaging (fMRI) time series. (Researchers employ time series from other imaging modalities to construct functional networks.) In figure 1, we show a pipeline of how to construct a functional network from fMRI time-series data
We present the results of our persistent homology (PH) computations to examine loops in functional brain networks

Summary

Introduction

Schizophrenia is a chronic psychiatric disorder that affects more than 21 million people worldwide [1]. It is believed that the cognitive deficits arise from compromised functional integration between neural subsystems [3,4,5,6]. There can be significant differences in the properties of the time series from imaging measurements of healthy versus schizophrenic individuals, different studies have found seemingly contradictory results when comparing functional magnetic resonance imaging (fMRI) time series from two distinct brain regions in a schizophrenia patient and a healthy control. The majority of studies have concluded that schizophrenia patients have less-similar time series than healthy controls across different brain regions [7]. Some studies have observed that schizophrenia patients have more-similar series than healthy controls across brain regions. Methodological steps in fMRI analyses seem to yield increases in these similarities, but abnormal neurodevelopment or drug treatment may play a role in increasing them in other cases [9]

Objectives

Methods

Results

Conclusion