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.