Fractal analysis of resting state functional connectivity of the brain

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.Comment: The 2012 International Joint Conference on Neural Network

Fractal-driven distortion of resting state functional networks in fMRI: a simulation study

Fractals are self-similar and scale-invariant patterns found ubiquitously in nature. A lot of evidences implying fractal properties such as 1/f power spectrums have been also observed in resting state fMRI time series. To explain the fractal behavior in rs-fMRI, we have proposed the fractal-based model of resting state hemodynamic response function (rs-HRF) whose properties can be summarized by a fractal exponent. Here we show, through a simulation studies, that the fractal behavior of cerebral hemodynamics may cause significant distortion of network properties between neuronal activities and BOLD signals. We simulated neuronal population activities based on the stochastic neural field model from the Macaque brain network, and then obtained their corresponding BOLD signals by convolving them with the rs-HRF filter. The precision of centrality estimated in each node was deteriorated overall in three networks based on transfer entropy, mutual information, and Pearson correlation; particularly the distortion of transfer entropy was more sensitive to the standard deviation of fractal exponents. A node with high centrality was resilient to desynchronized fractal dynamics over all frequencies while a node with small centrality exhibited huge distortion of both wavelet correlation and centrality over low frequencies. This theoretical expectation indicates that the difference of fractal exponents between brain regions leads to discrepancy of statistical network properties, especially at nodes with small centrality, between neuronal activities and BOLD signals, and that the traditional definitions of resting state functional connectivity may not effectively reflect the dynamics of spontaneous neuronal activities.Comment: The 3rd Biennial Conference on Resting State Brain Connectivit