The human brain is a complex neurobiological system characterized by nonlinear spatio-temporal dynamics. While functional magnetic resonance imaging (fMRI) has widely been used in the field of brain dynamics, the whole-brain nonlinear maps remain to be characterized.
We firstly applied phase space embedding on blood oxygen level dependent signals from resting state fMRI data. We mapped their phase space dynamics with SE, which is the sum of the length of the portrait edges. We studied the effects of repetition time (TR) and bandpass filter on the optimal model parameters, including the embedding time delay and the embedding dimension. The present method was applied to two psychiatric data sets, i.e., schizophrenia (SZ) and autism spectrum disorder (ASD), to demonstrate its capability in the characterization of abnormal brain dynamics. The statistically parametric maps were compared between patients and controls. A significant increase of SE was found in the default mode network, salience network, and auditory network regions of SZ patients, indicating increased dynamic change along with SZ. A significant increase of SE was also found in DMN and SN of ASD patients, besides the visual network. These results suggest that the present method is robust and promising in characterizing the dynamic changes of the BOLD signal among patients with mental disorders.
In addition, most of the fMRI studies which related to SZ and ASD had concentrated on the neuronal activity of patients in 0.01–0.1 Hz frequency band. However, it remains unknown whether underline dynamics in different frequency bands of BOLD signals in the two types of mental disorders. In this study, we firstly filtered BOLD signals into four sub-bands: slow-5, slow-4, slow-3, and slow-2. And then we used phase embedding to make more use of nonlinear dynamics on these multi-bands signals and calculated six geometric features in the embedding space. We used a SVM classifier to characterize SZ and ASD patients and we did a 10-fold cross validation with 100 initialization to compute mean accuracy. We achieved a highest accuracy of 85% and 73% for SZ and ASD, respectively. Out result proved that the present method is robust and promising in characterizing the BOLD signal among patients with two types of mental disorders.