Wavelet-based multifractal analysis of fMRI time series

Functional magnetic resonance imaging (fMRI) time series are investigated with a multifractal method based on the Wavelet Modulus Maxima (WTMM) method to extract local singularity ("fractal") exponents. The spectrum of singularity exponents of each fMRI time series is quantified by spectral characteristics including its maximum and the corresponding dimension. We found that the range of Hölder exponents in voxels with activation is close to 1, whereas exponents are close to 0.5 in white matter voxels without activation. The maximum dimension decreases going from white matter to gray matter, and is lower still for activated time series. The full-width-at-half-maximum of the spectra is higher in activated areas. The proposed method becomes particularly effective when combining these spectral characteristics into a single parameter. Using these multifractal parameters, it is possible to identify activated areas in the human brain in both hybrid and in vivo fMRI data sets without knowledge of the stimulation paradigm applied