EiDA: A lossless approach for the dynamic analysis of connectivity patterns in signals; application to resting state fMRI of a model of ageing

Abstract

AO_SCPLOWBSTRACTC_SCPLOWDynamic Functional Connectivity (dFC) is the study of the dynamical patterns emerging from brain function. We introduce EiDA (Eigenvector Dynamic Analysis), a method that losslessly reduces the dimension of the instantaneous connectivity patterns of a time series to characterise dynamic Functional Connectivity (dFC). We apply EiDA to investigate the signatures of ageing on brain network dynamics in a longitudinal dataset of resting-state fMRI in ageing rats. Previous dFC approaches have relied on the concept of the instantaneous phase of signals, computing the instantaneous phase-locking matrix (iPL) and its eigenvector decomposition. In this work, we fully characterise the eigenstructure of the iPL analytically, which provides a 1000 fold speed up in dFC computations. The analytical characterization of the iPL matrix allows us to introduce two methods for its dynamic analysis. 1) Discrete EiDA identifies a discrete set of phase locking modes using k-means clustering on the decomposed iPL matrices. 2) Continuous EiDA provides a 2-dimensional "position" and "speed" embedding of the matrix; here, dFC is conceived as a continuous exploration of this 2-D space rather than assuming the existence of discrete brain states. We apply EiDA to a cohort of 48 rats that underwent functional magnetic resonance imaging (fMRI) at four stages during the course of their lifetime. Using Continuous and Discrete EiDA we found that brain phase-locking patterns become less intense and less structured with ageing. Using information theory and metastability measures derived from the properties of the iPL matrix, we see that ageing reduces the available functional repertoire postulated to be responsible for flexible cognitive functions and overt behaviours, and reduces the area explored in the embedding space.