Sources of multifractality of the brain rs-fMRI signal

Based on the multifractal methodology, we examine how complexity in the dynamics of biological systems can be understood. The possible sources of multifractality have been determined by comparing the multifractal indexes obtained on the original, shuffle, Fourier transform surrogate (FTsurrogate), and iterative amplitude adjusted Fourier transform (iAAFT) time series. This paper shows that the rs-fMRI signal is multifractality. The multifractality is due to the fat-tail probability distribution, long-range dependence (LRD), and the excluded hidden structures. Although the excluded hidden structures also contribute to the sources of the multifractality, it is mainly composed of the fat-tail probability distribution and LRD, especially the fat-tail probability distribution. Specifically, the shuffle, FTsurrogate, and iAAFT series, those three series still display a multifractal behavior. However, based on the shuffle series, we know that the trend of change in the curve of fluctuation functions with q is significantly weakened, indicating that the probability distribution is not the only source of the multifractalionality of the rs-fMRI signal. In addition, the multifractal properties of the shuffle series are not as strong as the original series. The FTsurrogate and iAAFT series also are as powerful multifractals as the original. For the original series, the multifractal spectrum is an asymmetric bell shape, indicating that the multifractal spectrum is on the right. This means that the multifractality of the rs-fMRI signal in this scale range is determined by the multifractal properties of large and small fluctuations. The fat-tailed probability distribution, LRD, and excluded hidden structure are generated by the power-law distributions, scale-free temporal dynamics, and the highly structured dynamical activity in space and time (which means latent variables and connectivity patterns). This study implies that the study on the sources of multifractalionality may also discover new insights into the dynamic mechanism of spontaneous brain activity.