Fractal analysis of resting state functional connectivity of the brain

A variety of resting state neuroimaging data tend to exhibit fractal behavior where their power spectrums follow 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. This model provides a theoretical basis for the dependence of resting state functional connectivity on fractal behavior. Inspired by this idea, we 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). These estimators were evaluated through simulation studies and applied to the analyses of resting state fMRI data of the rat brain.

I. Introduction

The dynamics of endogenous neuronal activities has been an important issue in neuroscience since it is supposed to take control of most neuronal activities arising in the brain [1]. The huge default-mode functional network of the brain has been usually investigated through resting state neuroimaging data such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) [2]–[5]. One of the major goals in resting state neuroimaging research is the reliable inference of functional dynamics of spontaneous neuronal population activities from resting state neuroimaging data. However, it is not straightforward since resting state signals may be significantly affected by non-neuronal physiological factors. On the other hand, the response to stimulation in taskbased experimental paradigm is prominently correlated with brain activities either directly or indirectly.