Fractal analysis of resting state functional connectivity of the brain

TL;DR

This paper investigates the fractal properties of resting state brain connectivity using advanced models and introduces new estimators to distinguish fractal from nonfractal connectivity in neuroimaging data.

Contribution

It adopts the more general FIP model for fractality, introduces the concept of nonfractal connectivity, and develops wavelet-based estimators for analyzing brain connectivity.

Findings

FIP model effectively describes fractal behavior in neuroimaging data.

New estimators accurately distinguish fractal and nonfractal connectivity.

Application to rat brain data demonstrates practical utility.

Abstract

A variety of resting state neuroimaging data tend to exhibit fractal behavior where its power spectrum follows power-law scaling. Resting state functional connectivity is significantly influenced by fractal behavior which may not directly originate from neuronal population activities of the brain. To describe the fractal behavior, we adopted the fractionally integrated process (FIP) model instead of the fractional Gaussian noise (FGN) since the FIP model covers more general aspects of fractality than the FGN model. We also introduce a novel concept called the nonfractal connectivity which is defined as the correlation of short memory independent of fractal behavior, and compared it with the fractal connectivity which is an asymptotic wavelet correlation. We propose several wavelet-based estimators of fractal connectivity and nonfractal connectivity for a multivariate fractionally integrated noise (mFIN). The performance of these estimators was evaluated through simulation studies and the analyses of resting state functional MRI data of the rat brain.