The robustness of persistent homology of brain networks to data acquisition-related non-neural variability in resting state fMRI

Abstract

There is increasing interest in investigating brain function based on functional connectivity networks (FCN) obtained from resting-state functional magnetic resonance imaging (fMRI). FCNs, typically obtained using measures of time series association such as Pearson's correlation, are sensitive to data acquisition parameters such as sampling period. This introduces non-neural variability in data pooled from different acquisition protocols and MRI scanners, negating the advantages of larger sample sizes in pooled data. To address this, we hypothesize that the topology or shape of brain networks must be preserved irrespective of how densely it is sampled, and metrics which capture this topology may be statistically similar across sampling periods, thereby alleviating this source of non-neural variability. Accordingly, we present an end-to-end pipeline that uses persistent homology (PH), a branch of topological data analysis, to demonstrate similarity across FCNs acquired at different temporal sampling periods. PH, as a technique, extracts topological features by capturing the network organization across all continuous threshold values, as opposed to graph theoretic methods, which fix a discrete network topology by thresholding the connectivity matrix. The extracted topological features are encoded in the form of persistent diagrams that can be compared against one another using the earth-moving metric, also popularly known as the Wasserstein distance. We extract topological features from three data cohorts, each acquired at different temporal sampling periods and demonstrate that these features are statistically the same, hence, empirically showing that PH may be robust to changes in data acquisition parameters such as sampling period.

Keywords: TDA; fMRI; persistent homology; topological data analysis.