EiDA: A lossless approach for dynamic functional connectivity; application to fMRI data of a model of ageing

Dynamic Functional Connectivity (dFC) is the study of the dynamic patterns of interaction that characterise brain function. Numerous numerical methods are available to compute and analyse dFC from high-dimensional data. In fMRI, a number of them rely on the computation of the instantaneous Phase Alignment (iPA) matrix (also known as instantaneous Phase Locking). Their limitations are the high computational cost and the concomitant need to introduce approximations with ensuing information loss. Here, we introduce the analytical decomposition of the iPA. This has two advantages. Firstly, we achieve an up to 1000-fold reduction in computing time without information loss. Secondly, we can formally introduce two alternative approaches to the analysis of the resulting time-varying instantaneous connectivity patterns, Discrete and Continuous EiDA (Eigenvector Dynamic Analysis), and a related set of metrics to quantify the total amount of instantaneous connectivity, drawn from dynamical systems and information theory. We applied EiDA to a dataset from 48 rats that underwent functional magnetic resonance imaging (fMRI) at four stages during a longitudinal study of ageing. Using EiDA, we found that the metrics we introduce provided robust markers of ageing with decreases in total connectivity and metastability, and an increase in informational complexity over the life span. This suggests that ageing reduces the available functional repertoire that is postulated to support cognitive functions and overt behaviours, slows down the exploration of this reduced repertoire, and decreases the coherence of its structure. In summary, EiDA is a method to extract lossless connectivity information that requires significantly less computational time, and provides robust and analytically principled metrics for brain dynamics. These metrics are interpretable and promising for studies on neurodevelopmental and neurodegenerative disorders.