Spatially regularized wavelet leader scale-free analysis of fMRI data

Abstract

Slow brain dynamics has received considerable interest in the recent years, with the scale-free paradigm playing a crucial role for analysis of various neuroimaging modalities. However, assessing the role of slow arrhythmic fluctuations requires the use of a large continuum of time scales and thus of long time series, hence raising concerns regarding the use of scale-free tools on fMRI data. Further, scale-free analysis remained so far mostly univariate, that is, voxels are analyzed independently, hence neglecting their spatial organization. The present contribution aims to propose a spatially regularized estimation of the self-similarity parameter, based on a recently formalized formalism combining wavelet leaders and Bayesian models. The spatially regularized estimates permit to quantify the modulations of the scale-free dynamics from rest to a working memory task from fMRI data collected for 21 healthy volunteers. These modulations are significant in the default mode network and in some regions involved in task performance such as primary visual regions or the supplementary motor area.

Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives

“…By exploiting the time delay stability concept, the authors in Ivanov and Bartsch (2014) and Ivanov et al (2016) quantified the dynamic links among physiological systems and demonstrated a robust relation between the network structure and the physiological states. Moreover, despite numerous studies demonstrating the multi-fractal behavior of various biological processes (Goldberger and West, 1987; Stam and de Bruin, 2004; Wink et al, 2008; Bassingthwaighte et al, 2013; Delignières et al, 2016; França et al, 2018; Mukli et al, 2018; Racz et al, 2018a; Wendt et al, 2018), we lack mathematical and algorithmic tools for identifying the causal interdependence structure and the parameters of dynamical models of the type in Eq. (2).…”