Covariance and Correlation Analysis of Resting State Functional Magnetic Resonance Imaging Data Acquired in a Clinical Trial of Mindfulness-Based Stress Reduction and Exercise in Older Individuals

Abstract

We describe and apply novel methodology for whole-brain analysis of resting state fMRI functional connectivity data, combining conventional multi-channel Pearson correlation with covariance analysis. Unlike correlation, covariance analysis preserves signal amplitude information, which feature of fMRI time series may carry physiological significance. Additionally, we demonstrate that dimensionality reduction of the fMRI data offers several computational advantages including projection onto a space of manageable dimension, enabling linear operations on functional connectivity measures and exclusion of variance unrelated to resting state network structure. We show that group-averaged, dimensionality reduced, covariance and correlation matrices are related, to reasonable approximation, by a single scalar factor. We apply this methodology to the analysis of a large, resting state fMRI data set acquired in a prospective, controlled study of mindfulness training and exercise in older, sedentary participants at risk for developing cognitive decline. Results show marginally significant effects of both mindfulness training and exercise in both covariance and correlation measures of functional connectivity.

Keywords: correlation; covariance; exercise; functional connectivity; mindfulness; resting state—fMRI.