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Fractal analysis of resting state functional connectivity of the brain

Wonsang You, Sophie Achard, Jörg Stadler, Bernd Brückner, and Udo Seiffert
2012 International Joint Conference on Neural Networks, 2012
Publisher: IEEE
DOI: 10.1109/IJCNN.2012.6252657


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.


resting state, functional connectivity, fMRI, nonfractal connectivity, fractal, long memory, fractionally integrated process 


Further reading

  1. Wonsang You and Jörg Stadler, Fractal-driven distortion of resting state functional networks in fMRI: a simulation study, Brain Connectivity 2012, Vol.0, No.0, September 2012.
  2. Wonsang You, Sophie Achard, and Jörg Stadler, Fractal-based linear model of resting state hemodynamic response in fMRI, BMC Neuroscience 2012, 13(Suppl 1):P35, 21-26 July 2012.
  3. Wonsang You, "Long memory model of resting state functional MRI," PhD Thesis, Electrical Engineering and Information Technology, Otto-von-Guericke-University of Magdeburg, 2013.